Good afternoon everybody. My name is Adrian Dix. I'm BC's Minister of Health. Joining me today is Dr. Bonnie Henry, BC's Provincial Health Officer. We are honored to be here on the territory of the Musqueam, of the Squamish, of the Slavitooth people. We're honored to be giving this presentation today on their lands. Dr. Henry will give an update on how we're doing so far in this season of respiratory illness. And so Dr. Henry will be speaking first and then I will come up and give an update on issues around health system capacity, number of people in hospital, and so on. And with that is my honour for the first time in 2023. I introduce Dr. Bonnie Henry. Thank you very much and good afternoon. It is a pleasure to be with you here today. I'm also just want to recognize that today is a day that people are celebrating Black Shirt Day or in honour of the birthday of Martin Luther King on January 15th. And as I was thinking about this and thinking about the impact this pandemic has had on racialized populations, I thought a lot about some of the wise words that Martin Luther King spoke. And one of the things he said is that darkness cannot drive out darkness. Only light can do that. And hate cannot drive out hate. Only love can do that. And I think about driving out that darkness and how we are emerging from this last three years of this pandemic. So today I'm going to give an update on where we are in this respiratory season and to address some of the emerging issues and questions that have come up in the last few weeks, particularly around the new sub variants of Omicron, which I know many people are worried about, concerns around surges and other parts of the globe, and particularly China, and the impacts we are seeing of COVID. But also importantly, as we've seen through this last few months, RSV and influenza, and many other respiratory viruses that are causing illness. And as we've seen over this last month, some of the gastrointestinal viruses, especially norovirus, which we call winter vomiting disease, which I'm sure some people in this room have experienced in this last few weeks as well. I want to start by acknowledging that it has been yet another challenging time across BC and across Canada over this holiday period, not just because of the pandemic, but also impacts that we've seen of weather that made this another difficult season. And in many cases, kept us away from loved ones for yet another year. But I also want to thank everyone here in British Columbia who took the precautions that we needed to take over the holidays to keep themselves, their loved ones and their communities safe. Everything from getting your flu shot, to skipping those holiday parties if you weren't feeling well, to taking advantage of things like playing outside in the snow, and finding ways to overcome those forces that kept us apart with the new tools that we've learned over this last few years. All of your efforts have made a difference. In particular, I want to thank all of those who answered our call in November and December and took time out of their busy holiday schedules to get vaccinated, both for COVID and that all important, bivalent booster, and also for influenza. This has made a tremendous difference at ensuring we could manage and protecting those around us as well as ourselves. So many people in BC came together to support our health care system. We know that this pandemic has exposed the long-term strains on our health care system and on the people working within it. Of course, I know that many people unfortunately did get sick over the holidays, which put a damper on many of our plans. But we found ways to celebrate regardless in ways that we have learned in this past three years. In addition to many different respiratory viruses over the last few weeks, we've also seen a bit of norovirus, which has started to cause impacts both in our communities, but also in some of our health care settings. And while we're out of the holiday season, we're still very much in respiratory season. So today I'm going to give an update on where we're at with that, what we're seeing, and what a look ahead at what may happen in the coming weeks. To understand where we're at with all of these respiratory viruses, we in public health have many different sources of data that we look at sometimes daily, but also weekly. And we post many of these on the BCCDC website. And it is having these many sources of data that fill in this full picture. So no one thing tells us the whole story. It is all of these measures together that help us understand are things going up or down. Where are we seeing the pressure points in certain parts of the provinces? What are we seeing the different things? So I'm going to talk a little bit about each of these different measures. One of the most important ones we continue, people continue to be tested for COVID-19. And in our laboratories now, when somebody gets a test for COVID because of respiratory illness, we also test for RSV for influenza A influenza B and para influenza. We have one test that can do all of those. And about 1000 people a day on average have been getting a PCR test because they have a respiratory illness. And they are either in the emergency department, a clinic, a doctor sends them to the lab. And as I mentioned, we do these multiplex PCR tests so we can see what proportion test positive for these different respiratory viruses. That's one of the things that helps us understand what's causing illness across the province. So these are what we call medically necessary tests. We don't just test everybody, we test you when you need to have a test because it makes a difference for your medical treatment. So these are people who have serious enough illness that they seek medical attention, or people at risk of more severe illness from either COVID or influenza and are eligible for treatments, things like Paxilvid or Osiltamavir for influenza. A second most and more important other important source of information is data on people in hospital and ICU. And we have that data for COVID. It's taken a long time to get that. That's not something that we historically had for every other respiratory virus. But we've now added this year more information on people in hospital with influenza with RSV as well. And that gives us a sense of is this going up or down? What is causing most severe illness that's leading people to be in hospital or in ICU? We also need to remember that our behaviors have changed over the course of the pandemic. We're doing a lot more testing for respiratory viruses than we ever did before. So we can't compare necessarily to influenza seasons and RSV seasons that we had prior to this pandemic. A third source of data that we monitor that we put in place to help us understand this puzzle is outbreaks. So we look at outbreaks that are in healthcare facilities, including acute care facilities and long-term care homes. And those again are reported from different parts of the province. And that helps us understand spreading communities and impact on these most vulnerable settings. We also have a well established what we call Sentinel Providers Surveillance Network. And so the SPSM that's been started at the BC CDC way back in the early 2000s. And it is a way of that we've been using to help us understand people who go to see a physician or a nurse practitioner for an influenza-like illness. And so we follow physician buildings for that. And that's on the BC CDC website. That's that respiratory illness. And those people who participate in this, they do a swab on somebody who they think has influenza or COVID or RSV. And we test those in the lab for all of those pathogens and we do a whole genome sequencing on those. So I'll talk about that in a minute. So that's really important. That's been around for many years. That gives us a sense of what influenza-like illness, we call it, is in different parts of the province so we can break it down by health authority and geography as well. So along with the sources of data, we've expanded the work that we've done with whole genome sequencing, which is kind of new and exciting. And we had the expertise at the BC CDC, and you saw very early on in this pandemic, we were doing samples that helped us understand where the viruses were coming from, where COVID was coming from, because we could link them by the genetic code. We've expanded that program. And the Public Health Lab at BC CDC is now testing all of the cases that we get from people in hospital with COVID. We're doing whole genome sequencing on samples of people who have tests in the community from outbreaks. And this really gives us a sense of what strains we're seeing in BC and if they've changed. This is something that's new globally. We've never actually had this ability to watch a virus change in almost real time. And that has led to some of the issues that we have about what's the meaning of new sub variants. And I'll talk a bit about that in a minute. So our SARS-CoV-2 genomic surveillance is focused on identifying what variants are causing more severe illness. So we really want to make sure anybody who's in hospital, particularly because of COVID, but we test anybody who's been in hospital with a COVID positive test, we do whole genome sequencing to see if there's something that's emerging that's causing more severe illness. And we also do it on community PCR tests. And I said, and the tests from our central provider network. And along with this, we have the wastewater surveillance that we've started way back in 2020. And that was built on a platform of some work that was done with some of the key experts at the BCCDC prior to the pandemic. And we've been able to use that expertise to look at variants in different areas of the province. That's been in place, as we know, in the lower mainland. And that again is posted on the dashboard of BCCDC to help us understand, regardless of who's being tested, how much virus is out there. And not only that, but we now can do whole genome sequencing on those viruses that come from the wastewater surveillance plants. And that tells us, is there different strains in different parts or different variants in different parts of the province? We've recently added just over the fall, additional testing sites in interior health and island health, and those data are being validated. It takes time to develop, you know, the understanding of the nuances of the different systems.  And I think that's likely to be some time in February. We're also really interestingly in BCC, because we have this expertise in whole genome sequencing and the techniques of looking at wastewater, we're working to validate whole genome sequencing for influenza A and B, and RSV in wastewater, something that's novel, it's not being done around the country or around the world. So this will be something that will give us a sense in the future of what types of influenza we're seeing and where the burden of that is. And really interesting, and we have very little information on RSV in the past. So we're able to, we should be able to look at that too. As you also may know, the Public Health Agency of Canada has expanded its wastewater surveillance and to include YVR and we're partnering with them to do that. It's something that we've been wanting to do for some time, not just on flights from China, which helps us understand what strains are circulating there, but from other places in the world too. And I think this will be another piece that we can add to those things that we look at to help us understand what's happening and what's how it's changing over time. So like I said, it's like putting together a puzzle and all the different pieces for and part of the picture. So what is it telling us? In short, the good news is it's telling us that influenza continues to decline following this very strong early peak that we saw in November and December. RSV has continued to stay high. It's now at where we would expect it to see this time of year and it's leveling off. And COVID has remained relatively stable the past several months, and I'll just talk about these in a little bit more detail. So in terms of influenza, our data indicate from these various different sources that influenza in all age groups has steadily declined from the peak where we saw about 27% test positivity in late November down to we're about 5% now. So with all those tests that are done, about 5% of them are positive for influenza. This has been a very unusual year. So it is very important to recognize that we can't necessarily compare this year to previous influenza seasons prior to the pandemic. We knew and we talked about this in September and October that we saw a very similar unusual pattern in Australia and New Zealand during their influenza season last their last winter. And we knew that this was a possibility and that was one of the things that we were planning for and I know the minister will talk about impacts on the health system. So we did see that very rapid increase. And thanks to many people getting vaccinated and what we did, we've started to see decreases across age groups and particularly in children who have been affected by influenza as we know, leading to hospitalization in many, many children. And we know now that this is largely because there is a whole cohort, several cohorts of children who were never exposed to influenza because of all the measures we had in place. And particularly the restrictions on travel globally, influenza didn't spread through the first two years of the pandemic. So there's people whose immune system haven't developed that protection that they needed. The other thing that I think is important is that influenza A, H3N2 is the one that's been causing most illness and the one that's thankfully decreasing. And that is the strain of influenza that we see that most likely causes severe illness, particularly in children who've never been exposed to it before and in older people. And we also know that there are other strains of influenza and we often see later in the season that we'll see another wave of influenza B. So we're watching for that. And so far we've not seen a lot of it, but it does tend to happen later in the season. And it tends not to be as severe because most of us have had some exposure to influenza B at some point in our lives. And it doesn't change as quickly as influenza A. The other, so we're continuing to monitor that. We have, as you know, put in active surveillance to look for severe illness in children after the pediatricians, particularly at Children's Hospital, raised the alarm with us that they were concerned, that they were hearing about very severe illness and deaths in children in early December. And we have not seen any additional deaths beyond the six that were initially reported that we linked to influenza early on in the season. So that's important and thankful. So the other thing that I do want to mention is because we had such an early rapid season, our Sentinel Physicians practitioner surveillance network, we were able to do some vaccine effectiveness and that and the work that the BCCDC and Dr. Skrivonsky's team and it showed that early estimates show that the protection from the vaccine that we have right now reduces your chances of needing to see a physician or a nurse practitioner for influenza cuts that risk by at least half. So that's the good news. And for those who have not yet been vaccinated, it's still it's still available and important to do that. In terms of RSV, respiratory seasonal virus, while we are seeing a decrease in influenza, RSV remains relatively high, although it is also leveling off and is causing less illness in children, which is also important and good news. And it's about where we would expect it to be at this time of year prior to the pandemic. So RSV is another one of those respiratory viruses that when we stop travel and we stop gatherings and we had all of those measures in place, it didn't circulate very easily either. And now we're going back to a more normal season. And and unfortunately for us, the start of our RSV was at around the same time that we were seeing this this unusual and dramatic spike in influenza as well. So children who would normally have been exposed over the last two years weren't. And so they didn't have that immunity. And what we're seeing is it's again a cohort effect where there were many more children and slightly older children who were susceptible. And of course, as it started early on, and we know that that made a tremendous impact, particularly on children's hospitals. And just to remind people that the emergency departments are still busy. And they have put in place measures to make sure that we can quickly and effectively triage children.  But also know that your child's illness can be treated by a doctor's office, a walk in clinic, the urgent primary care centers, or if you need immediate medical advice, you can contact HealthLink at 811. And so finally, COVID is the other major one that's been added to the respiratory viruses that we are likely to see at least for the next number of years. And COVID-19 has remained relatively stable over the last three months. Hospitalizations increased a bit at the same time that we were seeing hospitalizations for influenza and RSV increase in December, but are now slowly coming back down. And we look again at the many different sources of information, and particularly things like the wastewater surveillance, which is not dependent on testing. And it shows a slowing and a decrease across much of the lower mainland, which is in keeping with the same thing we're seeing in visits to clinics, in long-term care outbreaks, and in the testing data that we have. So all of these pieces together tell us that we're slowly decreasing the same thing across time. And really, this is thanks to people stepping up and being vaccinated. I can't overestimate the importance of having those booster doses in effectively blocking the transmission in our communities. And along with that, I want to talk a minute about the XBB 1.5 variant, because it's been on a lot of people's minds over the last few weeks. To date, we've had 24 confirmed cases. So those are ones where the test has been done, and we've done the whole genome sequencing that shows it's this specific subvariant. And it's important to note that this doesn't reflect the total number of cases in the province. This is surveillance data. So this gives us a sense of what proportion of the tests that we're doing, the whole genome sequences, turn out to be this one. And we saw the first ones in late November, early December, and we now have found a boat. It's up to about 5 or 6% of the whole genome sequences are this variant. The most that we're seeing here, 95% of what is causing illness in the province is still the BQ 1.1. All of these are subvariants of Omicron. And I think that's really, really important. And while this XBB 1.5 has garnered a lot of attention, it still remains the subvariant of Omicron. So what does that mean? Any new variant that has an advantage spreads more easily. That's what viruses do. They change to try and reproduce themselves more quickly. And if it spreads more easily, it often will replace the ones that went before it. So each new one that spreads, by definition, is the most infectious one to date. And we've seen that with XBB 1.5. So why does it take off in some places and not in others? A lot of it has to do with the defenses that we have in our community. And importantly, there is no evidence that this subvariant is causing more severe illness. And there's very good evidence that our vaccines are still providing strong protection from serious illness and death, especially if you've had the bivalent booster that has that Omicron antigen in it. So if you have not yet had that, then you need to get it. So we must remember that these new strains may make us more vulnerable to infection, but they don't render us defenseless. The defenses we have built through immunization and combinations of vaccine immunity and infection induced immunity means we have strong defenses as a community across this province. We are no longer in the place where we needed to take extraordinary measures because everybody was susceptible and many, many people could get seriously ill, need hospital care or die. And as we talked about hospitalization due to COVID-19 is decreasing. And even though it is decreasing, we know our hospitals are stretched. It's not surprising this time of year. We traditionally experience an increase in hospitalizations in January as people access care after the holiday period. And it often coincides with an increase in respiratory illnesses. And usually this is when we would start to see influenza really taking off as well. People delaying seeking treatment over the holidays because of the weather is one of the issues or in challenges in accessing care. And again, of course, surgeries ramping up again after the holidays slow down. And also I will mention we've been seeing norovirus. So this gastrointestinal illness causing effects as well. So as we get back into our regular activities following the holidays, it is important to continue to take measures to protect ourselves and others from respiratory viruses and other infections. First and foremost, getting vaccinated, getting that booster dose if you haven't already. These boosters make a difference. If you're feeling unwell, whether it's from a respiratory virus or fever and a rash or GI upset, nausea, vomiting, stay home, stay away from others and particularly avoid contact with people who are more vulnerable to severe illness themselves. It's so important and I say this how many millions of times to regularly wash your hands, practice proper respiratory etiquette, covering our coughs, properly disposing of tissues. We can also wear masks, especially in crowded indoor spaces when there's poor ventilation. You can wear masks for yourself for additional protection if you're somebody who is more at risk and for others. If you have mild symptoms of what could be a respiratory virus or is still recovering or have had contact with somebody at home who's ill. I know this remains a challenging time for people who are most vulnerable to COVID, especially. And these are the same people who are more at risk for severe illness from influenza and from other infections too. While we know we cannot stop all transmission viruses, even with broad measures like masking all the time, stopping gatherings and travel. And we know these measures have very important negative health impacts too. What we do know is that having the high rates of vaccination and hybrid immunity that we have protects everyone. And the analogy that somebody said to me the other day was, you know, would you rather be the only person vaccinated in your community or the only person unvaccinated and everybody else in your community is vaccinated? And that's an important thing to think about because all of us being vaccinated gives added protection for those who don't have a strong response to vaccine and it gives a buffer so the viruses can't spread as easily. What we do protects those around us and makes it harder for the virus to spread. Not completely, not 100%, but definitely harder. We've seen the impact of that. We know it's never going to be 100%. So we all need to be mindful of others who are more at risk, given space. Use the tools that we have, all of the tools that we have, postpone non-essential visits if we're not feeling well. Wear good fitting medical or N95 masks if you need that extra protection. Ensure people at high risks are able to access some more masks too. And we have been very clear about ensuring that everybody has access to booster doses, to their flu shot, and to access to treatments for both COVID and influenza. So I'm just going to finally say respiratory illness will continue. Generally we start seeing it leveling off into February and by March so we're not out of the woods by any means yet. But if we all continue to do these things, to use all of our tools to be respectful and mindful of each other, we will get out of this season in the best shape possible. I want to thank everyone for their continued commitment in BC to protecting themselves, their loved ones, and their communities during this respiratory illness season. Another challenging time for us as we work to emerge from this pandemic, emerge into the light, and return to those important activities in our lives. Thank you very much. Thank you very much, Dr. Henry. And I wanted just to bring you an update on the emergency operations centers around the province and the challenges we're facing in acute care and the very significant successes we're having with respect to surgery in our province as well. Starting this week on January 9th as I informed you last Friday, the five health authorities and the regional health authorities and the PHSA have reactivated emergency operations centers throughout the province to provide enhanced supports for staff and patients at 20 of our hospitals. This proactive test step has taken to ensure patients continue to have access to the hospital care services they need in these challenging times of respiratory illness and other things facing our healthcare system. More people in hospital reflects obviously more people with severe illness in the community. The health authorities have already set up, were already set up to launch into actions that will best need the patients, needs of patients in their regions. Most of them have scheduled dedicated leadership teams as well as adding ICU physicians, hospitalists, patient care coordinators to be present seven days a week. The EEOC teams are focused on reviewing hospital bed availability, identifying solutions to ease emergency department congestion and supporting patients who are ready to be discharged from hospital, helping them to transition in a safe way. They are working on key actions to increase efficiency such as improving the triage process in emergency departments, further implementing quick response teams to connect patients with care in the community, increasing the integration with urgent and primary care centres, supporting rural and remote care and transport, and improving communications about services for patients. We're also expanding, continuing to expand the capacity for long-term care beds and opening transitional beds for an alternate level of care patients, people who are still in the hospital that are essentially their needs would be better served in long-term care. This is the first week of operation and already a tremendous amount of work has been done and I sincerely thank everyone involved our extraordinary healthcare professionals and workers for their efforts. And because we're in the first couple of weeks of January, which is typically when we observe our census in hospitals closely, we expect there'll be continued fluctuation in the numbers as we move forward. I wanted to give you an update on those numbers. Last week when I was here, I reported on 10,226 people hospitalized in BC. As of yesterday at midnight, end of day yesterday, that number was 10,116, needed a hospital bed. This represents about 87% occupancy rate of the total base and surge beds, but as you will know also 110% of base bed capacity in the province. This is obviously the week when we see our highest census, but we also saw significantly higher census than we typically see in the week between Christmas and New Year's. With emergency operation centers in place and the return of healthcare workers after the holiday, we are also able to see more availability and ability for patients to go to urgent primary care centers and to their primary care providers. But our hospitals are busy, even historically busy and people can be assured in spite of those circumstances when they need hospital care, they will receive it. I wanted to give you an update on surgeries and in the questions, we are happy to also report on specific actions taken in specific regions, but we want to obviously get to questions today more quickly. Further, many of you, and there is interest I think in people in media for their communities, will be providing once a week on Thursday per hospital data. So we are providing it today per hospital, later today what the data is, number of beds, number of people in hospital each of our hospitals in BC and then we are providing it after that every Thursday. So you will have that detailed information on a consistent basis. I want to give you an update on surgeries. Over the week from December 18th to December 24th, which is typically a slow week, health authorities performed 4,698 surgeries in BC just to put that in context during the same week in 2019, and there is an influence of statutory holidays here before the pandemic. The number of surgeries performed was 2,574, so that's a significant and historic number of surgeries completed, even as the health system faces these challenges. But I would add the previous week, December 11th to 17th, health authorities completed 7,463 surgeries in a time when many of you and many people reporting the challenges of the health care system. We are completing more surgeries than in any week at any time in the history of the health care system in British Columbia. And the previous week to that, it was 7,343, that's the week of December 4th to 10th, that's the fourth highest in the history of the BC health care system, breaking the records we set in October. What that suggests and says is that extraordinary work is being done by our health care workers and health care professionals. And our system on the issue of surgeries because of the efforts we've collectively made all of us with respect to surgical renewals have helped people get the surgery they need when they need it. I also want to say because we do postponed surgeries, so in the context of that record number of surgeries, some surgeries were postponed and from January 1st to January 7th and this reflects situations in particular hospitals, health authorities postponed 190 non-urgent scheduled surgeries, that's 116 in Fraser Health, 26 in Interior Health, 23 in Island Health, 2 in Northern Health, 18 in Vancouver Coastal Health, 5 in the Provincial Health Services Authorities and that includes 2 at Chavisee Children's Hospitals and 3 at BC Women's Hospitals. As we've noted in the past, we moved very quickly and a very significant number of those surgeries will be rescheduled and done very soon. As you know when we cancelled tens of thousands of surgeries earlier in the pandemic, 99% of those have been completed and our EOCs are there to support surgeries to continue. Also, I just want to note finally all of the efforts and acknowledge the really remarkable job our pharmacy sector has played and our public health sector in providing people with vaccinations. I just want to put it in context, we have now total doses administered in terms of influenza is 1,722,583 as of January 12th, that is an all-time record in BC and that effort includes 35% of those aged 6 months to 5 years or 4 years and 364 days and that is a significant increase from where we were when we made the appeal to people to get vaccinated and have their children and bring their children to be vaccinated. Early in December, I think it was 22% in that category at that time, it's now 35%. This is a significant achievement. There are appointments available everywhere. I encourage people to continue to get vaccinated against influenza, continue to get vaccinated against COVID-19, but I want to particularly recognize the role of pharmacy in our fall campaigns as they've completed 2,287,000 vaccinations of COVID-19 at pharmacy, COVID-19 or influenza, which is an enormous contribution. As all of you know, because almost many of you here will have been vaccinated, we do those one at a time, so that's a real achievement for everyone in the healthcare system. We want to thank everybody. I think it's critical to remember in closing that all of us have continued to have a role play as Dr. Henry has said. It's important to stay home when we're sick and that's why we have the first legislative sick days in our province. It's important to wash our hands frequently and get the booster you need for COVID-19, a flu shot as well when you're eligible. We need to keep doing what we know and keep doing what we know works. And with that, I invite Dr. Henry back to the podium. We're happy to take your questions. Thank you. After three years, we finally have a nice podium over here. Thank you. As a reminder to reporters in the phone, please press star one to enter the queue. You are limited to one question in one follow-up. Please also remember to take your phone off mute. You are not audible until your name is called. Our first question is from Katie da Raza van Kuversen. Hi, Minister. This is for Minister Dick. Thanks for taking my question. I want to ask about Bill 36 because some physicians have expressed concerns about what they say is government overreach. So they've expressed concerns about government having more access to their medical records or more power to need out more severe discipline against physicians. What do you say to these concerns? Thanks very much for the question and the opportunity to respond on this question.  But if you want more, Katie, I have to give you a call later because there'll be other questions as well. I know Bill 36 is the first reform of the Health Professions Act in 30 years, considering the changes in healthcare in that time. It's a timely and important reform. It came out of a very significant report done by an expert in the field, Harry Keaton, that was done in response to concerns about certain health regulatory bodies, or one, the dental profession and how it was conducting certain aspects of this business, and a broader review of how we regulated health professions. We followed that up with an all-party process. In other words, the Liberal Health Critic at the time, the Green Party Health Critic and I, reviewed the Keaton report and developed a series of recommendations which became Bill 36. We had an extensive public consultation, one of the most expensive, extensive on legislation. The province has ever seen thousands of participants. The majority of them health professionals, including of course many doctors, many others as well. The legislation does important things. It takes a proactive approach to eliminating discrimination in BC's health system. The in-plane site report and the Reconciliation Act happen in the middle of our consultations around Bill 36. We improved governance. We've reduced the number of regulatory college, so they all have the ability to, I think, do what they're required to do into the law more easily. When I became Minister of Health, there was a regulatory college that had to support all of the activities of regulation with 87 providers, and so we are shifting that. It's our expectation there'll be six colleges at the end of this process. And more transparency and accountability, something the public had been asking for and many journalists such as yourself had been asking for. In other words, not when there are complaints made, but when there are findings of misconduct that those findings of misconduct be published. And that is a reasonable step that was massively supported in our consultation. So I'll speak to a couple of the issues you raised that are issues of concern that have been raised in the last couple of days. First, it talks about that there's been concern about patient clinical records that somehow this will give somebody in government a chance to seize or copy a patient's clinical records. This is not true. It is false. Bill 36 does not allow the government to copy or seize clinical records. Only an independent investigator appointed by the independent registrar, the request of the investigation committee can do so. When there's a complaint, for example, a complaint of abuse, you have to be able to review the evidence to provide to determine the validity of that complaint. When a healthcare professional has a complaint against them and it has warranted an investigation, therefore it's a significant complaint, the investigator requires the ability to search records to act in the public's interest, but is also subject to restraints on how that information can be used. Let me be very clear. This is no different than the circumstance in the present act. No different. There has been concerns about what physicians and other health professionals can say. Again, with respect to putting forward false information, which sometimes happens, for example, false information about the effectiveness of certain remedies, there is a requirement to be truthful and evidence based now. That is a professional requirement that all, in particular, physicians support. That will continue to be the case. This isn't about a critical, this is about limiting critical or free speech. In fact, it's what the legislation supports what we do now. You can't put out false information as a professional. I don't think anybody really would be concerned about that. Finally, I just say with respect to the way we appoint people to regulatory colleges. We've had 22 regulatory colleges when I became Minister of Health. We've reduced that number and amalgamated number. It's now 15. It will eventually be six. Currently, at the discretion of the Minister of Health, the Minister of Health, in the case of myself, before it was Terry Lake, would appoint 50% of the board members. And the profession would elect at these 23 different colleges, their board members, from the profession. Now, these colleges do not represent the profession. They represent the public interest. So they regulate the profession. So the recommendation that was overwhelmingly supported in our consultation was to move to a merit-based system where you have the superintendent making recommendations on people who are qualified to act on health college boards. And that is the core of it. So it takes away discretion from the Minister of Health as it goes through that process and from the professions themselves who are being regulated by that process. This was overwhelmingly supported by all three political parties who took part. By the vast majority, I think 92% of people who took part in our consultation. And that's what the Act reflects. And I think that there can always be criticism and always better ways to do things. We started this process in 2018. It's a five-year process, most significant consultation, Indigenous consultation reflecting the requirements of the Reconciliation Act and the in-plane site report, massive consultation of health professional organizations including all of the ones involved reflected in the 22 existing colleges, a significant consultation of the public, and a reflection of the views of many, including people in the media, about removing some of the opaque elements of the current Act. I want to say to everybody, though, complaints don't get made public. It's only when determinations of misconduct are made that they should be made public. And they should be made public in every case. And that's the determination that's made. But that's after a lengthy process where all sides have the opportunity to state their views. So that's the bill. It's a significant bill. It's all laid out in the legislation. Much of what a significant portion that was in regulation is now in legislation. And I think it's a good thing for people. Katie, do you have a follow-up? Yes, please. When you talk about the people appointed to the college, the colleges, would they be people in the industry with knowledge of that particular profession, or would they be anyone? How do you select who's appointed? The expertise is developed independently. So we appoint an oversight body to make sure, because we had 22 on out of six with health regulatory bodies, with too much variety in standards and so on. So this will be a merit-based process, expertise in regulation and understanding of regulation, how to deal with complaint process, and to ensure that justice is brought to those processes, not just for health professionals, for health professionals and patients. So that's the reason we're doing it that way. Right now, we, of course, attempt to do that and I think do a relatively, a very good job in doing that. But the discretion, for example, in this process, and the recommendations and the fact that those recommendations will be public. And right now, half of the people are appointed directly by me. And well, I think we've done a good job. And I think previous ministers have done a good job in appointing really good people to those boards. This professionalizes that process. This happens frequently with boards everywhere. And I think that's a good thing. Next question is from Richard Sussman, Global News. Dr. Henry, would you say that we are beyond the peak now of the new season? And what are the expectations moving forward in terms of what we can expect for flu and RSV and COVID? One of the things you mentioned when you were talking about masking mandate is, quote, there are very negative health impacts as well. Can you talk me through what you see as the drawbacks of the mandate in terms of health impacts? Sure. So in terms of influenza, we have seen a very unusual season where it's been compressed from what we usually see over several months in November, December, and we have seen a decrease. But as I mentioned, it's been H3N2 almost exclusively, very little of any other strain. So we are watching because we can see a surge of influenza B often later in the season, just the way it circulates. But influenza B tends to have less severe illness in most people and less of an impact. So we are watching for that over the next few weeks. In terms of RSV, I do expect it to continue its leveled off and we'll see it coming down. Thankfully, it's come down in children and we're seeing it more in some long-term care homes and in adults right now. So the normal trajectory for RSV will, for it to fade away over the next few weeks. And with COVID, what we're seeing is relatively steady. And that's the good basis of protection that we have. And so, leading to your second question, when I talked about the negative consequences, it was all of the measures that we had in place. So mass mandates in all settings, reducing of gatherings, closing of schools, things that had, we know, negative impacts. And if we look at countries like China where they had very intense and strong COVID-zero measures in place for a long time, we see that there were tremendous negative impacts on people for a whole variety of reasons. And we saw some of that from the limited closures that we had in place here, mental health anxiety. And we're still seeing the repercussions of some of that in people who need assistance in mental health issues in particular. So it wasn't masking by itself that has the negative consequences that I was referring to. It was the measures that were in place. And I think we need to be realistic and recognize, and we can look at China as a good example of that, that even with all of those intense measures in place, this virus has changed so that it can spread. There's no way that we can stop 100% of infections with the strains that we're seeing circulate. And we see that with influenza. We see that with RSV as well. So we need to put it in the context that we are in now, where we have this very high level of protection because of the immunity that we have from vaccination, from previous infections, and the tools that we have that we can use in our individual way to fit them into our lives as we're getting back to doing the things that we need to do. And it is incredibly important for us to get together, to be together, to go to work, to have those gatherings. We're social creatures and we know that there's important emotional, mental, physical health things that come with us being together. And so we need to take what we have learned and put it in the context of what we're doing in our lives and our risk and do those risk assessments for ourselves and for the people around us. And that's what we need to do to get us through this respiratory season. And we need to learn these things for the future as well. Did you have a follow-up Richard? I do. Dr. Erdinger with a shortage in our healthcare system in terms of staff, we've seen over the last little bit increase in terms of the number of a very vocal minority calling for you to make changes around the vaccine mandate for healthcare workers in the hospital system. Is there any consideration that would be given to that? And to that point, is the requirement now two vaccinations of a COVID vaccine? And does that not offer in essence the same amount of protection at this point considering that second shot could have been a year plus ago as being unvaccinated? Would there be a consideration given to ensure that those working in the healthcare system are up to date on their boosters as well? So the short answer is no. We're not contemplating changes to the requirements of vaccination in our healthcare system.  And we know how important it is to have that protection individually, but also collectively around supporting each other in the healthcare system. So we are looking at moving away from that being an order under a public health or provincial health officer order to that being part of our routine regulations around people who are working in our healthcare system. And it is what we as healthcare workers are committed to doing everything possible so that we stay healthy and that we are able to protect our patients as best we can. In terms of the concept of immunity, what the requirement is and will continue to be is a primary series. So whatever that primary series is, and for most people, that's two doses of vaccine. As we know, after the primary series, things have become complicated and that's because the virus has changed. We know that we have a high level of people who've had mostly mild, thankfully, infections from from Omicron over the last little while. So it is we have various different types of immunity and different people. So it's not as simple as saying you need to be up to date with you need to have a booster because it may be that people have had their primary series, they've had an infection that gives them some hybrid immunity. And we know that now we're learning as we go along that that gives some longer term protection. We know from our serology that many people have a combination of both vaccine-induced protection as well as infection-induced protection. And so it's much more difficult to put in a place of standard that says you must have this. So it is a combination of those things. But overall, all of the data that we have shows that if you have at least that primary series in the context that we're in right now, your risk of having severe illness, your risk of being hospitalized, is considerably less. It was four to eightfold less than people who have not had any vaccines at all. So it still is an incredibly important measure and it's important where we need it most in our health care system. Next question is from Wolf Defter, Black Press. Yeah, hi. Good afternoon. Thank you for taking my question. I appreciate it. A question to the minister. What if any timelines do you have in place to help bring down some of these capacity numbers that you mentioned earlier? Are you looking at these figures within two weeks within a month? What if any sort of internal deadlines have you sort of put yourself for that? Well, the Emergency Operations Centre will be in place for six weeks. That doesn't mean it will take six weeks. We would hope to see fewer people in our census numbers in the hospital. But just to be clear, what we're trying to do, we're trying to ensure that patient flow is there and supports are there for our health care workers, our health care teams, workers and professionals and for patients to ensure that they get care at this critical moment. There's a lot of people in hospitals. This is historically a high level of people in our hospitals. That was true between Christmas and New Year's and comparing to other seasons and it's true now. But what we don't want to do and what we want to avoid and what we want to continue to do is do high numbers of surgeries. So we're providing care because if you defer treatments for any reason, then you have to make that up later for the system. But for people, it's very hard when you defer surgeries. So we did defer some surgeries this week in particular locations. We also did an extraordinary number, a historically high number of surgeries. So what we want to do is continue to provide the care people need in the province and take down, we hope of this period, the number of people in hospitals. A lot of that though is related to, I mean, we always get questions about COVID-19. Dr. Henry just talked about the requirement to be vaccinated. The issue isn't requirements, the issue is COVID-19. The issue is respiratory illness or the issue is that there are a number of people who need care. And so what those high numbers reflect is the extraordinary work of healthcare workers and healthcare professionals in providing unprecedented amount of care. We're doing vastly more surgeries than ever before, I argue, vastly more diagnostic tests, more primary care visits, treating more people in the hospital, more people in our ERs. And after three years of a pandemic, and it's getting on to three years now, our healthcare teams, in spite of the constant pressure that's existed, no high season and low season, just constant high season of pressure. There's been a lot of pressure on all of them. So we're trying to do everything we can in this period to deal that and support it, but the EOCs will be in place for six weeks. Wolf, did you have a follow-up? Yes, the system is under such high pressure as you say. Why not take, and these were touched on this a little bit earlier, but why not take more precautionary measures? Obviously, I answered earlier, 100% transmission or preventing 100% of transmission is not possible, but why not aim for 90? Why 100% of the threshold, say 90% is available? Anyone could argue that any amount could make a difference on the health system if it is so strange. Yeah, so I think you have to put it in the context of where we are. So we do have the best protection that we have through vaccination. That level of immunity in our communities is that buffer. That means that COVID is not causing any more severe illness than other respiratory infections. And so to try and incrementally reduce transmissions above that, we would have to take additional measures that would impact people's ability to do important things in their lives. So we would have to stop large groups, stop large gatherings, reduce the numbers of people who get together, restrict travel, all of those things that have negative impacts on people's health as well. So there's no one simple thing. So everybody wearing masks is not going to make a tremendous difference in the transmission of these viruses because we transmit them in those situations when we're at home, when we're with friends, when we're doing social things that are important in our lives where we don't wear masks. And it still allows these viruses to transmit. So the most important thing that we can do as a community, and people in BC have done this, is to get vaccinated, to get that protection. That gives that level of buffer the best that we can do. And then to each of us take our own responsibility for protecting others. We're staying away from others if we're sick. If we are having mild symptoms, we need to be around others, wear a mask. And those of us who are most at risk, we can do extra protections ourselves by avoiding going to certain situations if we can by wearing a well-fitting mask or respirator if we have to be in those more risky situations. And this is how we managed respiratory seasons before. And now COVID has added to that. It's another virus that we have to deal with. And we are in a very different situation. And it would be nice, it would be really nice if there was just one simple measure that was going to make that difference. But it's not. It's all that collective things that we are doing and continue to do a need to continue to do together. Next in the line is Lisa Yuzda, CD News 1130. I think if we can expect next year to be an easier season of respiratory illness, does the rough year this year and kids catching up on catching these illnesses, is that portends of an easier one next year? Or does it take a while for that community, I guess, exposure to gain again? I wish I could answer that question. One thing that I've learned in the face of SARS-CoV-2 is humility because it changes. However, we have been relatively looking at the tea leaves and watching what's happened over the last few months. Things have progressed as we kind of thought they would, and we're sort of seeing less and less variation and severity of illness. So we need to keep watching for that. And yes, I expect that there will be some impact of the fact that so many more children were exposed to RSV, so many more people were exposed to influenza, but then again, influenza likes to change too. So I can't really say. I will say that we're watching around the world. We'll be watching what happens in Australia and New Zealand this year. But we do know that the most single most important thing that we can do is keep our immunity up by getting boosters when we need to, by getting our flu shot every year. And so I think we just need to keep on watching and we'll see what happens in the next little while. Issa, did you have a follow-up? I do. And just over the next, I guess, four or five weeks when the EOCs are going to be open, but over the next four or five weeks, what are your biggest, what is the biggest concern? Is it one virus more than another? Is it overall, and just wondering what the biggest worry is? You know, I think it's not one virus over the other. I think we need to pay attention to all of them. And as I was talking about today, you know, there's these many different things that we watch over time to see if things are going up or down or staying the same. And and then we add in that whole genome sequencing to see if there's something new or different. And every time there's something new or different, we have new technology that allows us to say things about it. And so, you know, one of the reasons why there's such a concern about the new variants is that, you know, we do things like neutralizing antibodies, and they're really easy to do. And people say, oh, it's more transmissible, it binds stronger. But those are things that come out first. And then over time, we actually put it in the context of everything else. So I think it is all of these. And for me, it's not just, it's the fact that respiratory season is here. And it is adding a burden to an already stretched system, as the minister was talking, but we've not had any downtime. It's been high level through the summer, and now in respiratory season. So it is part of what is causing the strain on our system. But it's certainly not the only thing. So those two things are together. We're seeing normally this time of year, we would see a lot of other reasons why people start going into our hospitals, sometimes for delayed care, sometimes because of weather issues. And we're also seeing that on a base that's higher than normal. Because we now have COVID, we now have a new virus that's added to our repertoire that we're going to have to deal with for the next foreseeable future. Next question is British Tea Bassoon, Capital Daily. Thank you for my question. Dr. Henry, you mentioned there's been a surge in norovirus and gastrointestinal issues in NBC. Given studies that show that gastrointestinal problems can be symptoms of COVID, are people showing up with GI issues at hospitals being tested for COVID? Yes, so the things that we see for COVID tend to be quite different. Norovirus is a very particular problem and people are being tested for it and it spreads very rapidly for anybody who's had the experience of it. So the clinical pattern of what we see with norovirus, for example, is quite different from what, from some of the GI symptoms that can present with SARS-CoV-2 as well. So the short answer is that they look different and they're tested differently as well. Priestie, did you have a follow-up? Yes, thank you. Minister Dix, can you share how many surgeries were postponed between January 7th and 11th across BC and also specifically in Island Health? And is postponing surgeries the reason why hospital occupancies dropped by over 200 over the past week? Well, first of all, it didn't drop by over 200 in the last week. That's not the case. It dropped by, I think, I think it was about 120. And the answer is no. We've been doing more surgeries than ever before and we're going to continue to with our surgical renewal commitment. We put it in place by adding operation in-room nurses, adding anesthesiologists, adding medical device reprocessing technicians. And so that's the reason we did all of those things. I listed off the numbers from the December 1st to 7th. But what we do is under different circumstances, surgeries can be postponed. For example, a team of people that's performing the surgery test positive for influenza or COVID-19, the surgery and that slate of surgeries would have to be postponed. And there is of course more illness in the system. But in a general sense, and we provided the information for January 1st to 7th and we'll provide the analysis of this week and next week in terms of surgeries postponed. Number of surgeries postponed is relatively low as compared to the very significant number of surgeries taking place, the record number of surgeries taking place. So no, it's true that if we decided to have more people wait for their surgeries, we might bring down somewhat the number of people in hospitals. But that would also have a profound effect on all those people. We are very reluctant to delay surgeries and that's the reason we continue to do record numbers of surgeries. December was an extraordinary achievement by our surgeons, our nurses and our health sciences professionals, our healthcare workers. And I think everyone should acknowledge that. I don't think anywhere else in Canada, maybe the world we see in such a difficult time, such an extraordinary performance. It's one part of what we do in the healthcare system. The final thing I'd say is that surgeries themselves, it would only affect the number of what we'd call non-urgent surgeries that require overnight stays. So that's not the reason why we've seen a decline. But what I would say about the numbers is that there's a decline of about 100 from where we were last week. It's still dramatically high. We still have hospitals in BC notably, in Kelowna and Kamloops in Richmond and in other communities in Burnaby and communities in BC that are above base and surge beds capacity, which is and our teams are doing an exceptional job managing that situation. So I wouldn't say that the number of people in hospitals today is a low number. It's a historically high number. It's just slightly lower than it was last week. The last question from Benoit Ferradini, CBC Radio Canada. Thank you for taking my question. And the first one will be about the Paxilovid drug. I'd like to know how much of the stock of those doses of drugs have been used in BC so far? Is it still around 16% and what are your thoughts about letting it being prescribed by pharmacists as it's the case in other provinces? If possible, I'd like to have the answer in English and French. Sure. So we have a clinical care committee that provides the guidelines on use of medications like Paxilovid, particularly as the evidence around its use was increasing. And as you know early on, we had limited amounts of it, so it was available only in specific centres and we put in place a centralised process for people who didn't have a physician to be able to get access to it if they needed it. We've now expanded that quite a bit since about the summer. I don't have the exact numbers of doses that have been used, but I know that it is much more available. People do have access to it much more widely. It can be prescribed by any physician and it's available in pharmacies across the province, and we still have in place the centralised intake centre where you can talk to a pharmacist about whether it is a medication that is compatible with the medication you're on and your health conditions. Paxilovid is a challenging drug because it does have many what we call drug-drug interactions and people with certain conditions, particularly depending on their renal or kidney function and liver function aren't able to take it necessarily. So the data that I know is that about half of people who are assessed for it, who might benefit from Paxilovid, are not able to take it in discussions with their clinician because of the medications they're on or because of their health condition. In terms of pharmacy prescribing, I understand Ontario just started that relatively recently. What we have in place here is still that it is prescribed by a nurse practitioner or a physician, but it's available through pharmacies and we have pharmacy consults to help people who don't have a primary care practitioner have access to the medication as well. Minister Dix will do all the French at the end. Benoit, do you have a follow-up? The follow-up will be from Minister Dix as well and it will be French and English. She already touched about that, but if the influenza peak is behind us, what is the forecast for the next week's month about how the hospital will keep busy and how long will we need the EOC staying active? I'll just talk to the influenza piece whereas the first peak. So we still need to pay attention to influenza because we know that we often see influenza B start to circulate around this time. So we're watching for that. So it is one of the pieces that adds to the burden of people who need hospital care. It's also something that affects long-term care homes in particular. We know influenza can cause very severe illness in long-term care homes and we're seeing outbreaks in long-term care from influenza also settle down. So that's good news in the short-term. I'll let you talk to the impacts. And it's just because it may have reached its peak and we'll see. We learn about these circumstances every day. It's still significant in the system. I think people would understand that even if it was, say, 374 last week and it's 320 or something this week, 320 is still a significant number equally for RSV influenza has gone down in the system. So you asked how long the EOCs will be in place six weeks to ensure that we're managing the system through this time and we're doing the maximum we can to help people and get them the care that they need. Well, you'll note last January and at previous times, early in the pandemic, particularly, we delayed the non-urgent scheduled surgeries and we do that in individual cases now and I laid off the numbers and just in response to the previous question that was 23 last week in Vancouver Island Health Authority in total. And so we're doing that but we're trying to maintain a maximum response because we know people who need surgery need surgery as much in January as any other time and we want to deliver that. So that practice that we engaged initially to defer all non-urgent surgeries has now been significantly adjusted and was during both the Delta and the early Omicron variant of concerns cases. So we deferred fewer surgeries in those times and now we're actually and have done in December with all of this going on had the most extraordinary month of surgery we've ever had in the province of B.C. and that's a real tribute to all our health care workers. Thank you very much. I'm going to be making a report on our early efforts to expand the scope of practice of pharmacists. I talked a little bit about vaccination but the efforts so far have been extremely successful and we're very positive about what's happened and the work that professions are all doing to provide care to people across B.C. of course we'll be adding to the that scope of practice later this spring for from pharmacy and from pharmacists. But I think it's fair to say that our pharmacists have done exceptional work this fall both in supporting people and getting the prescriptions they need and in providing vaccination. Thank you. That's all the time we have.


This is the Van Gogh self-portrait right here. But check this out. I'm a researcher and producer of this technology. So, this technology, we have developed cognitive science. And so, in this technology, only just illuminating the shadow and the color, sorry, the shadow and the light. You told me how it works. It was magic. Oh, I know the trick. But that's really beautiful. This is an illusion. Can you put this in the museum? Put it near the future. And you can do this with any painting. Automatically, you detect the shape. You put it exactly where it is. Look at that. You can eliminate the 3D structure. It's beautiful. It's very cool, right? So, is this new? Yeah. First time you show it? Yeah. What we will do in the future? This is for advertisement and promotion. Promotion, yeah? Like this. This is advertisement in Japan. That's nice. But Van Gogh is something. Yeah, and so... Beer. Beer and steak. Yeah, but I think... In partnership? Yeah, I know. And put on every painting? Yeah. One month? I want to do it. And one month, every painting will be alive. Yeah. How much work? Yeah. I want to do... How much work? To do for one painting, something. Oh, yeah. It's about an hour. One hour? One hour? Yeah. One hour. Only one hour? Yeah. Editing software. Oh, let's look... So you analyze, you show it in faces? That's right, yeah. And you have different patterns? Yeah. We have... We can create many patterns. Of course. Yeah. Also on the original? Yeah. It depends on the... It depends on the performance of the projector and the environment. You should make partnership with the... It depends on the light, you know? You should make partnership with Las Vegas. Okay? Las Vegas Hotel can just make copies of every famous painting. Yeah. They can just take a copy because they can have every famous painting and you can have a special show. Live. Get all the famous paintings to come alive. And the waves. That's it. That's it. That's it. That's it. That's it. That's it. And so in addition, this picture is very, very finest. Finest. Finest. In the world. Very good imitation. Yeah. Finest. Yeah. Who made this? Finest. Yeah. Who made this? Yeah. This is a maker. What yoghurt is that? COI site. Reproduction at Tok University. So that's a great idea. The Sun Museums with very good reproductions. That can come alive.


Yeah, that was a nice first match. I got Gared in as a my oppo and Alex setting along with bossy and Tanner those four guys I wanted that was my goal for that match is to have them start and play a complete match because they've been training really hard and pushing the other unit and and not only training hard, but they've played in key matches To get us to this in the number four ranking So I felt good about the Wilkes match. I left landing in just as you know our captain just kind of You know stabilize the team and I had who else Reynolds just short on middles Yeah, I'd say Um Arcadia played really great. I mean they blocked us and we never you know returned the favor So Yeah, you know we had we ended to ran into passing trouble Towards the end of the match Couldn't really run our middles get first set our middles were like unstoppable and then But then as the match went on I think You know they actually did a better probably out past us and and when you know their middles hit better They probably hit better all around we kind of rent our offense kind of slowed down and And became too predictable Yeah, it's a tough loss. I told the guys it's a long season I don't really pay that much attention to the polls It's nice to be ranked high and and they deserved it. They had a really tough kind of preseason But you know our goal is to win the Mac and so we hope to play in the Mac Finals and we should if we're playing better and I Think the guys that played against Wilkes are gonna make The other units stronger as we go along here and and so I'll be playing those guys too. I Don't intend to just have a one-starting unit say per se and we play miserable. Yeah, I think and Is it Eastern? Yeah, they're there are new teams So so I think I'm confident I can put anybody out on the floor and and compete against those teams So those guys needs everybody needs time on the floor. So I think that's approach. I'm gonna take Well, it was a good match I mean if they like volleyball that those are the kind of matches that we're gonna have against Arcadia well not again here, but well maybe here in the final and then You know, there are other teams that are strong in our conference messiah Alvernia So, you know come come out it helps the team when yet when they're chairing and we'll put on a better show next time


We are learning numerical methods for first order initial value problem. In this, we have learnt Euler method and Runge-Kutta method. In this class, we will introduce two methods. One is midpoint method and another one is trapezoidal method. We will use a different idea to derive these two methods. We will first write the initial value problem in the form of an equivalent integral equation and then use quadrature formulas to approximate the integrals appearing in this equation to get these two methods. One is a two-step method and another one is an implicit method. Let us go to derive these two methods. Recall that the initial value problem that we are interested in is given by y dash is equal to f of x comma y and this equation is posed on a closed and bounded interval a comma b and we are also provided with an initial condition y of x naught equal to y naught where x naught is a point in the interval a comma b. Often we take x naught equal to a just for the sake of simplicity. Recall we have derived the forward Euler method in one of our previous lectures where we have approximated the derivative y dash in our equation using forward difference formula and thereby we got the formula for the forward Euler method as y j plus 1 equal to y j plus h into f of x j comma y j. Here you can see that in order to get y j plus 1 we just need to know the value of y at the previous node that is at x j. So, in that way this method is a one-step method and also you can see that y j plus 1 is obtained fully from x j and y j which are known to us. In that way this formula is an explicit formula for y j plus 1 and that is why we say that the forward Euler method is an explicit method. Well we have obtained this formula by approximating y dash by the forward difference formula. Now we can also get the same formula using another approach here what we will do is we will write the given equation in the equivalent integral form. How are we getting this? Well we have y dash is equal to f of x comma y right. Now you integrate it from x j to x j plus 1 the same has to be done on the right hand side also right x j to x j plus 1 d s. So, let us write it as s d x j plus 1 d s. And this is d s right. Now here you can see that the integral becomes y of x j plus 1 minus y of x j which I will take on the other side y of x j plus this integral is kept as it is x j to x j plus 1 f of s comma y of s d s. So, that is what we are writing here. So, this equation can be equivalently written in this form we are just using the fundamental theorem of calculus for that you have to of course assume that f is a continuous function with all this nice assumptions you can see that the given ODE is equivalent to this integral form of the equation. Remember this is not a formula, but it is a equation because you have y on the left hand side which is unknown and that is evaluated in terms of again y which is sitting in the integrand here. Therefore, it is an integral equation and it has to be solved in order to get y. Now we know that there are some integrands f for which we do not know how to perform this integral explicitly in which case you can approximate this integral by a quadrature formula. So, that is the idea. Now what we are claiming is that there is a quadrature formula for which we will get the forward Euler method. The question is what is that quadrature formula when I replace this integral by that quadrature formula leads to forward Euler method. Let us see if you recall we had studied a rule called rectangular rule. So, what it says integral a to b f of x dx is nothing but b minus a into f of a. So, that is what we are going to use here integral x j to x j plus 1 f of s comma y of s ds is equal to x j plus 1 minus x j into f of x j that is the value of the function f evaluated at the lower limit of the integral ok. And we know that this is nothing but h therefore, this can be written as h into f of x j comma y j. Now you replace this integral by the rectangular rule and thereby you get y j plus 1 remember since I put an approximate expression for this I will not use the notation y of x j because this is used to indicate the exact solution. So, I will use this notation to indicate the corresponding approximation to the exact solution and that is given by y j which is an approximation to y of x j plus this integral is now replaced by the rectangular rule and that is precisely the forward Euler method right. So, the forward Euler method which we derived by replacing y dash by the forward difference formula can also be obtained by replacing the rectangular rule in the equivalent integral equation. Now from here we get lot of ideas because why only rectangular rule we can also replace this integral by midpoint rule, trapezoidal rule, even Simpson's rule and Gaussian quadrature rule right. So, we have many formulas from which we have scope to get many methods this is what is the interest for us in this lecture as the first step let us consider the integral form of the ODE here, but there is a slight difference in the way I have taken this limits I have taken the limits as x j minus 1 to x j plus 1 remember how you will write this integral equation is up to you you just have to integrate y dash of s d s integral f of s comma y of s d s and then take any limit. So, it is not necessary that you have to take x j to x j plus 1 you can also take x j minus 1 to x j plus 1 like that you can take the integral over any interval, but only thing is you have to take the same integral on the right hand side also right. So, that is what I am doing here why am I doing here with a different limit because I want to now apply the midpoint rule if you recall midpoint rule is given by integral a to b f of x d x is integral a to b f of x d x is actually b minus a into f evaluated at the midpoint of the interval that is b plus a by 2 right. Now, when I want to apply this midpoint rule to this integrand I have to evaluate this integral at the midpoint of the interval on which you are taking this integral and that midpoint should coincide with one of your grid points that you have generated in your problem that is why I have taken the limit as x j minus 1 to x j plus 1. So, that x j is the midpoint of this interval remember we always work with equally spaced nodes again this is only for the convenience, but here we are crucially using it and that will make the evaluation of this quadrature rule exactly at the node point x j for that reason we have chosen this you have to choose similarly for Simpson's rule also because Simpson's rule also evaluates the value of the function at the midpoint of the interval right. So, in such cases you have to make sure that all the points where you are evaluating the function should be the grid points of your problem. Once you have this now it is very easy for you to apply the midpoint quadrature rule for the integral and that is given by this which is nothing, but 2 h into f of x j comma y j right. So, when you apply this quadrature rule into this equation you get the formula y j plus 1 equal to y j minus 1 plus 2 h into f of x j comma y j that is why you have 2 h here because you have applied the quadrature formula in the interval x j minus 1 to x j plus 1 ok. You have chosen a wider interval in order to fit this function evaluation exactly at a grid point ok. So, this is the idea of midpoint rule well we have the midpoint method for our initial value problem and we have the following important observations about this midpoint method what are they the first observation is that to compute the value of y j plus 1 we need to know the value of y j and not only that it also depends on the value at x j minus 1 right. Therefore, y j plus 1 depends on the value of y at 2 grid points one is at x j and another is x j minus 1 that is the first observation. Now, when you go to find y 1 how will I get it well put j equal to 0 to get y 1 that will make the first term here as y minus 1 what is that it is nothing, but y evaluated at x naught minus h. But if you recall we have posed the problem only in the interval x naught to b right we do not care about x naught minus h it is outside our domain. Therefore, we do not know whether the solution exists at this point or not even if it exists we have no interest to calculate the value of y at this point. So, we cannot go to use the value at this point that makes the method to be not applicable for j equal to 0 in that case therefore, you have to compute y 1 using some one step method something like forward Euler method. Once you have y 1 from some other method then we can use y naught and y 1 to obtain y 2 using the midpoint rule and similarly you can use y 1 and y 2 to get y 3 from the midpoint method and so on. So, you can apply the midpoint rule only for obtaining y j for j equal to 2 3 and so on whereas, y 1 has to be obtained from some one step method like forward Euler method. Such a method is called a two step method because to find y j plus 1 you need to know the value of the solution at two previous nodes right here it is y j and y j minus 1. Let us take an example where we have the initial value problem as y dash is equal to y and y of 0 is equal to 1. Our aim is to obtain an approximate value of y of 0.04 with the step size h is equal to 0.01. As we have already observed we have to use some one step method to obtain y 1. Here we use the Euler's forward formula and get the approximate value at the point y of 0 comma 0 1 as 1.01 and is denoted by y 1. So, we got the value of y 1 from forward Euler method. Now to get y 2 we can go for the midpoint method y 2 is from the midpoint method given by y naught plus 2 into y 1 h y 1 and we know all the values. Therefore, we can plug in all these values and get the approximate value of y of 0 comma 0 2 and it is given by 1.0202 here. Similarly, you can also get y 3 y 3 is the approximation to y of 0 comma 0 3 and it involves the values of y 1 which is we have already computed from the Euler method and it also involves the value of y 2 which we have computed from the midpoint tool from here. So, you can plug in those values and get the value of y 3 which is approximately 1.0304. Similarly, you can get y 4 which is the approximation of what we want. So, we want y of 0 comma 0 4 and that is now given by approximately 1.04081. Now let us see what is the exact value of the solution y of 0 comma 0 4. You can clearly see that the exact solution is given by y of x equal to e power x from there you can compute the exact value of the solution and that may be taken approximately as 1.040811. So, that is pretty close to what we have obtained also. You can see that we have obtained the approximate solution up to 6 digit rounding with respect to this exact value the error is given by this which is pretty small. If you recall we have also obtained an approximate solution for this initial value problem using forward Euler method and for the same value of h that is h equal to 0.01 we got the error from the forward Euler method as this value. From here you can see that at least in this example the midpoint method performs better than the forward Euler method. So far we have only derived explicit methods where the unknown y j plus 1 is obtained as a solution of y j and y j minus 1 which are already computed when we go to compute y j plus 1. In that way the methods that we have derived so far are explicit methods. There are also other cases where the unknown y j plus 1 is obtained as an implicit relation involving known and unknown quantities such methods are called implicit methods. Let us illustrate such a method by putting the trapezoidal rule to the integral equation. Just recall that the trapezoidal rule for this integral is given by b minus a which is x j plus 1 minus x j by 2 into f of b that is f of x j plus 1 comma y j plus 1 plus f of a which is f of x j comma y j. So, we just have to replace this integral by the trapezoidal rule and we get y j plus 1 equal to y j plus h j plus 1 minus h j is precisely h for us divided by 2 into f of a plus f of b. This relation is called the trapezoidal method here you can see that we obtained a relation for y j plus 1 and it is implicitly represented because to get y j plus 1 we again need to know y j plus 1 on the right hand side also. If you recall both in the midpoint rule as well as in the forward Euler method we obtained y j plus 1 purely in terms of the known quantities whereas, in the present case we only have an implicit relation and for this reason this method is called an implicit method. Note that the trapezoidal method can be explicit if the function f is linear in y. Let us see this by an example consider the initial value problem y dash equal to x y and the initial condition is given by y of 0 equal to 1. Here you can see f of x comma y is equal to x y and you can see that f is linear in y. Let us take h equal to 0.2 that is not very important for us now we will apply the trapezoidal method to this initial value problem and see that we get an explicit relation just because f is a linear function in y. Let us see how it goes recall the trapezoidal rule for this initial value problem is y j plus 1 is equal to y j plus h by 2 into x j y j plus x j plus 1 y j plus 1. Of course, we have y j plus 1 appearing on the right hand side, but what you can do is you can take it to the left hand side and then you can easily solve for y j plus 1. So, that is what we do here for instance y 1 is given like this and when you plug in all the known quantities here we have this expression where y 1 is again not known to us, but that does not matter you can take this y 1 to the other side and get an explicit relation for y 1 like this and that immediately gives you the value of y 1 as well. So, therefore, as long as the right hand side function f depends linearly on y you can still use the trapezoidal rule just like the explicit method. In fact, you can also get y 2 very easily again y 2 will be given in terms of y 2 again, but that is again appearing linearly therefore, you can solve it to get y 2 and that value is given by 1.0842. Now, the question is how to solve this in general trapezoidal rule gives a non-linear equation for each y j plus 1. Let us see this by another example. Now, let us take the initial value problem y dash equal to e power minus y with the initial guess as y of 0 equal to 1. In this case y 1 is given by this expression where the right hand side also involves y 1, but now it depends on y 1 in non-linear way. Now, it involves y 1 in terms of the exponential function. Now, it is not very easy for us to solve this equation to get y 1. Now, the question is how to solve this non-linear equation at every grid point? There are two ways that we can handle this problem. One is to use some non-linear iterative method. Let us first consider the non-linear equation. The non-linear equation is precisely y 1 which is coming from your left hand side minus 0.1 into e power minus y 1 minus you collect all the constants in one place and that is equal to 0. Therefore, you have this non-linear equation g of y 1 equal to 0. You have to solve this equation to get y 1. If you recall, we have learnt some non-linear iteration methods in one of our previous chapters. So, you may use one of those methods to obtain a solution to this non-linear equation which will be the approximation to the solution of your initial value problem at x equal to 0.2. This is one way to handle this non-linear equation. Let us put this idea in a general way. How to proceed when we are working with implicit methods? Because implicit methods in general gives us a non-linear relation involving the unknown y j plus 1. The idea that we have proposed in the last example is to go for one of the non-linear iterative methods. Recall that the trapezoidal method is given like this. This equation can be seen as a fixed point problem where the iteration function g of y is given as y j plus h by 2 into f of x j comma y j. These are known quantities plus f of x j plus 1. This is also known comma y. So, this is unknown to f. Therefore, you can define the iteration function like this whose fixed point is precisely the point y equal to y j plus 1. So, that is what we are seeing from the trapezoidal method. So, that is what I have written here. We can view the trapezoidal method as a fixed point iteration method Now, you can choose any initial guess which we will denote by y j plus 1, 0 and then define the fixed point iteration method like this where you will plug in y 0 and get y j plus 1, 1 and again plug in y j plus 1, 1 on the right hand side get y j plus 1, 2 and so on. So, in that way you generate a sequence of numbers which is expected to converge to the fixed point of the function g and that is precisely the approximation of our solution at x j plus 1. There is another approach which is called the predictor character approach where you take the initial guess from the Euler method. Remember in the first approach you get the initial guess arbitrarily whereas, in this we are taking the initial guess from the Euler forward formula which is called the predictor step and then use this value here to compute y j plus 1 using the trapezoidal method and that step is called the character step. In that way you have one predictor step get the initial guess from the Euler forward formula plug in on the right hand side and thereby the expression now becomes explicit you can find y j plus 1 from there and that is called the character step and such a method is called the predictor character method and since we are using Euler forward formula here and then computing the solution from the trapezoidal method this method is also sometime called as Euler trapezoidal method. Let us take our previous example y dash equal to e power minus y on the interval 0 to 0.4 with h is equal to 0.2 we are given the initial condition as y of 0 equal to 1. We will now compute the solution using the Euler trapezoidal method that is the predictor character approach which includes one predictor step which is coming from the Euler forward formula and that is given by this value. Now you plug in that value into the trapezoidal method and perform the character step and get the value as 1.070966. Similarly we can do the step 2 for step 2 again you will take this value y 1 remember do not take this value for the predictor step of y 2 ok. So, you have to take the character value from y 1 and plug in that to the predictor step of y 2 and you get the corresponding value once you get that value you just plug into the character step and get y 2 from here and that gives us the value for y 2. So, this is not the value for y 2 it is just a prediction and that is further corrected by the trapezoidal method. So, this is a nice illustration for the predictor and character method in this lecture we have learnt two important methods one is midpoint method which is a example for a two step method and another method we learnt is the trapezoidal method which is an example of an implicit method we will continue our discussion on multi step methods with explicit and implicit forms in the next lecture. Thank you for your attention.