ity and also political thought. I absolutely welcome Maggie Chapman's challenge to every single member in this Parliament to design an economy as if people mattered. We need to take on the big issues here. We need to think about restructuring our economy. We have got lots of lessons to learn. I think that that is why an independent public inquiry called forbouts called Hamilton and many other members is absolutely pressing. I think that the most obvious lesson that all Governments around these islands and in Europe have to learn is that we did not treat this virus as a SARS virus. We treated it as a flu virus and, as a result, major mistakes were made. The previous Covid committee in the last Parliament took evidence on this. Professor Woolhouse from the University of Edinburgh said, and I quote, we did our homework, but when we were given the exam it was the wrong test. Governments simply got it wrong. They planned for a flu virus. It was something far more serious than that. We also took evidence from Professor Baker, who led New Zealand's response to the virus. They admitted that they got it wrong early on as well. They were caught on the hot. They did not have adequate planning, but they were prepared to learn. They learned very quickly from the experience in China. They learned very quickly from the evidence that came out of the Taiwanese plan to tackle the virus back in 2003. What they did was put their flu plan effectively in reverse. They threw everything at Covid in the beginning, instead of what we did, which was to gradually increase the response as the virus worsened. We have serious lessons to learn here. I think that back to March last year, when unfortunately our chief medical officer at the time was on the TV advising people that it was perfectly safe to go to six nations matches. I think that we need a long hard look at our preparedness for dealing with pandemics in the months to come. However, we must become more prepared for the future. We finally got that testing capacity. The Greens made that case early on that we needed to ramp it up. That will be critical now in dealing with the later stages of this pandemic and preparing for the future. We need to ensure that there is proper support for people to do the right thing and self-isolate as well. No one should have had to choose between going to work to earn a wage and self-isolating. Although the self-isolation grants, the criteria for those grants will widen twice as a result of green pressure in the last session, we are still seeing high levels of people being rejected from receiving those grants and still having to make that choice between going to work and doing the right thing. The BBC had figures last night on the TV. 45 per cent of people were rejected in recent months from those grants. There should not be a question of entitlement to benefits. Those grants should be available instantly at a decent level and they should be universal alongside a package of wider support to help people to do the right thing whenever there is a pandemic. We have had a wide-ranging debate this afternoon. I want to point out an important point about the challenges that young people have around exam style assessments. Let us go further in that. Let us question why we have exams full stop. Why can we not have continuous assessments? We need to think big in terms of education in closing the attainment gap. Members have also talked about the huge toll on business that we have seen. We have all seen that. I have seen it in my high street in Stirling as well, shops closing down. However, the way to avoid that cycle of lockdowns would have been to have taken the bold move early on to have a full lockdown to get the virus under control. The point that is made by Anna Sarwar is that yes, business needs that certainty going forward. We need to get back into a regular cycle of announcements from the Scottish Government and Parliamentary Scrutiny. It is important that the machinery of this Parliament gets up and running again. We have a Covid committee that can go through the data and take expert evidence and assess the restrictions on a week-to-week basis. That is something that we have to do as a cross-party basis, and we will do that. In terms of the health service, I think that Gillian Mackay absolutely nailed it. It is about fair pay, but it is also about the working conditions. It is about moving away from the crisis management that we have seen with mental health and the drugs crisis that Michael Marra spoke about as well. That defining mission that Gillian Mackay spoke about, the national care service, has to be at the heart of this Parliament's work. I would like to finish Paul MacLennan's John Muir quote, the power of imagination makes us infinite. Thanks for reminding us about that. Absolutely, that is what we should be aiming for, aiming for the stars. Mr Ruskell, could I now call on Jackie Baillie to close for the Labour Party? Thank you very much, and I welcome you, Deputy Presiding Officer, to your new role. Can I also congratulate all those who have made their maiden speeches today? All of them were fantastic, but let me pick out three in particular, from Pam Duncan Glancy, from Sandesh Gulhaini and from Michael Marra, and say to my colleagues that this has raised the bar for all of us. I very much look forward to working with Gillian Mackay in the health portfolio. As many have said, the last 15 months have been some of the most challenging that many of us have ever experienced. I want to begin by sending my condolences to everyone who has lost a loved one through Covid and to thank NHS, social care and council staff who have worked so hard to keep us safe. Over 10,000 people in Scotland have now died of Covid-19, well over a third of which were care home residents. Each loss is devastating, and many people with no underlying health conditions ended up on life support machines, showing just how seriously each and every one of us must continue to take this. What is particularly hard to come to terms with is the scale of death within our care homes. The way that our older people and care home staff were treated, who worked round the clock caring for us, is nothing short of a national scandal. Figures are still emerging, which show the true extent of the impact of Covid in our care homes. The families of those who died, as well as the staff, deserve answers. That is why a public inquiry is essential. I do not think that we can wait for a four nations inquiry. Many of those decisions were taken exclusively in Scotland. We need an inquiry in Scotland. I think that we all watched in a degree of shock yesterday as Dominic Cummings outlined the chaos at the heart of the UK Government. What is true is that the approach taken by the UK Government was mirrored in the early stages of the pandemic by the Scottish Government. Let me illustrate that with a channel for interview about herd immunity. Scotland's national clinical director, Jason Leitch, was asked, do you agree with Sir Patrick Vallance, the chief scientific adviser, that one of the aims of the UK Government is for people to develop some immunity to this disease? Jason Leitch's response is, I do. I absolutely agree with him because we have no choice. The SNP went along with some of the decisions of the UK Government that was exposed yesterday by Mr Cummings. Michael Marra rightly said that the Government failed to deal with the pandemic quickly enough. That cannot be allowed to happen ever again. However, what started out as a health crisis very quickly became a crisis affecting every part of our society—our economy, our education system and normal everyday life. Businesses have gone to the wall. Many are still struggling to survive. Thousands of workers lost their jobs immediately and hundreds of thousands were put on furlough. GDP has fallen by a staggering 8.4 per cent. Unemployment has risen to 123,000. For some of the 300,000 people on furlough, there is a potential for more job losses as this unwinds. The scale of the challenge is huge. It is more significant than the banking crisis that took 10 years for the country to recover from. Unfortunately, the challenge that we face is not yet matched by the scale of the ambition that is required by the Government. Let me illustrate this by talking about fair start Scotland. Just 14 per cent of those enrolled in the first three years of fair start managed to sustain employment for more than 12 months. What is even worse is that more than 13,000 people had left the scheme early—almost 3,000 more people than the number of participants who actually started a job. There is no point in introducing a job scheme if the majority of people do not end up in sustained employment. We are facing a very real impending jobs crisis and the SNP's existing programmes lack ambition and will not deliver for the scale of the challenge required. Scottish Labour set out plans to guarantee every young person and the long-term unemployed and those with a disability a job in the public sector for six months in a comprehensive programme to tackle the jobs crisis. However, we also need action to help businesses to remobilise, to stimulate growth and to reinvigorate our tourism and hospitality sector so vital to jobs and the economy. Scottish Labour suggested a £75 debit card to spend on our struggling high streets. We also had exciting proposals for a great Scottish staycation, both of which I commend to ministers. However, turning to education, our young people have had a really tough time. They have been out of school for the best part of the year, isolated from their friends, missing out on education and opportunities. Our young people cannot be made to suffer any longer, yet they face a second year of chaos with their school qualifications, which is causing anxiety and misery to thousands of families across Scotland. I know that the cabinet secretary has left the education portfolio, but I hope that he would agree that it is essential that his replacement publishes the appeals process next week. We must have a reset guarantee for all affected pupils and the Scottish Government must work with colleagues in colleges and universities to ensure that no young person misses out as a result of the pandemic. Turning to the NHS and social care, there is no doubt that the work done by staff at the front line of the pandemic was truly heroic. Many of them went to work without adequate PPE. They put themselves in their families in danger whilst doing their very best to care for us. Many of them are now considering early retirement because they feel burnt out. That will have a huge impact on remobilisation plans, but workforce capacity is not a new problem. The Scottish Government has been told about workforce capacity many times over successive years, but the problem is not yet fixed. Nicola Sturgeon, when she was health secretary, was warned by the RCN and the BMA that cuts to the number of nurses and doctors who would have severe consequences, but she did not listen and now the NHS suffers as a result. Pam Duncan Glancy rightly made the point that many problems existed before the pandemic, but Covid made it worse. It has served to heighten inequalities. Nowhere is that more obvious than in access to mental health services. We need an urgent increase in in-patient, out-patient and crisis mental health services, and we need it because we face an impending crisis. Waiting times were also bad before the pandemic. They are even worse now. 62 patients were waiting for treatment in 2012 when the treatment time guarantee of 12 weeks was introduced. 62,000 are waiting now. We also know that at least 7,000 people have cancer, but they have not been diagnosed and they have not been treated. A catch-up programme is urgent or people could lose their lives. We have made a number of suggestions that I will talk about when we debate the recovery of the NHS next week. Let me conclude by talking about the Government's cross-party Covid recovery group. We need to look at recovery in the short and the long term and we need to recognise that Covid will still be with us. I look forward to making a contribution to that group. However, we need to plan for the continued suppression of the virus. That means targeted business support. That means robust testing and tracing that responds rapidly to outbreaks. That means improvement to the self-isolation grant and that means ramping up vaccinations. There are 980,000 doses of vaccine allocated to Scotland that remain unused. We are behind Wales, we are behind England in the vaccination programme. There is no doubt that, while Scotland and the UK stockpiled vaccines in Wales, they got the vaccine into people's arms. I welcome the health secretary's promise to speed things up and I would recommend mass testing and mass vaccinations, especially in areas such as Glasgow. We on the benches will work with the Government, the business community, our colleagues in local government, the voluntary sector and those in the health and social care sector to build a recovery, to build that fair in Scotland. However, we will be critical of the Government if they fail to heed the lessons that they need to learn about our recovery. I now call on Annie Wells to close for the Conservatives in around 10 minutes. Thank you, Deputy Presiding Officer. I, too, would like to welcome you to your new role. Today's meeting speeches were fantastic meeting speeches. There are a couple of ones that, again, I would like to pull out of there. Pam Duncan-Clancy's speech was phenomenal, passionate and powerful, as was Dr Sandesh Gulhani. However, everyone's speeches right across the chamber have showed what a breadth of talent that this Parliament has and has gained more of. I would also like to congratulate John Swinney on his new role and congratulate my fellow Glasgow MSP Humza Yousaf in his appointment as Cabinet Secretary for Health and Social Care. To oversee that vital portfolio is a huge responsibility in normal circumstances, but to do so with Scotland remains amidst the global pandemic is truly a significant challenge, and I wish you well on that. I would also like to stress that my appointment as Shadow Cabinet Secretary for the Conservative Party, alongside my brilliant team, Sandesh Gulhani, who gave again a very powerful made-in-speech Sue Weber and Craig Hoy, I am open to having constructive relationships with the Government where possible. However, the Cabinet Secretary will also be aware that my Scottish Conservative colleagues and I will not hesitate to hold the Government accountable when there have been clear shortcomings. Assessing where we currently are as a country in our battle against Covid, the light at the end of the tunnel is certainly getting that bit brighter. Thanks to the sheer brilliance of the scientific community, both at home and internationally, each dose of the vaccine is steadily guiding us towards freedom, which I am certain that we will never take for granted again. The vaccination route has been a success story in Scotland and the United Kingdom as a whole, demonstrating the overwhelming benefits of working together to emerge from the pandemic. However, as my colleague Murdo Fraser highlighted, there remain significant and difficult questions to answer, particularly if maximising uptake as we proceed down the younger age groups. There is no question that vaccines are our best route to reducing restrictions, which continue to have a huge impact on Scotland's economy, especially in Glasgow, where many businesses have been quite frankly struggling to survive. To echo what has already been said loudly and clearly by the Scottish and UK Governments, when you get the call, go and get the jag. As we all know, the NHS has been placed under immense strain, and yet, even before the pandemic began, there was serious concerns over the NHS backlog. As we look to emerge from the immediate threat of the pandemic, the NHS backlog is at great risk of spiralling out of control. While there is rightly been a focus within our NHS on tackling Covid, it is also true that thousands of non-Covid-related appointments, treatments and operations have been postponed due to the pandemic. It was revealed only this week, as shown by the latest Public Health Scotland statistics, that around 28,000 patients have spent 52 weeks or more on NHS lists awaiting planned hospital treatment. Meanwhile, as of March 2021, around 100,000 Scots are still waiting on key diagnostic tests. Leading charities such as Cancer Research UK have already expressed deep concern over the on-going backlog of individuals waiting to receive critical tests and receive a diagnosis. To consent this challenge head-on, the Scottish Conservatives called for an additional £600 million to tackle the NHS treatment backlog in 2021-22. Suffice to say that the NHS continues to face one of the most challenging periods in its history. The substantial impact of failing to tackle the backlog will be felt by tens of thousands of people across the country, and it must be a top priority for the cabinet secretary if we are to avert a full-blown healthcare crisis. The impact of Covid-19 on our social care system has also been felt by thousands across Scotland. For too long, this cruel virus has meant that families of care home residents had been separated from loved ones and were unable to give them support, even so much as a hug. Since the beginning of the pandemic, the Scottish Conservatives have consistently pressed for a judge-led public inquiry on over the 3,000 deaths from coronavirus in Scotland's care homes. The last Parliament voted for this twice, but it was ignored. That has been an unprecedented pandemic, so, of course, mistakes have been made. However, the actions taken by ministers at that time must be properly scrutinised. The reason behind these crucial mistakes must be established, particularly in regard to moving elderly patients from hospitals into care homes. The Government has a responsibility to give those families who have lost loved ones tragically passed away from Covid in care home settings. They deserve the closure not only that they need, but they do frankly deserve it. Looking ahead to the future of social care reform in Scotland, the Scottish Conservatives support many of the recommendations that have been put forward in the failure review, including viewing social care as an equal part to the NHS. I look forward to engaging in further discussion with the cabinet secretary, councils, families and providers on the matter in the coming weeks. The issue that remains very close to my heart, and one that has been exasperated by the pandemic, is the drug death crisis in Scotland. It is time that we took meaningful steps towards ending this. In my area of springburn, I have saw first-hand the impact that drugs have on victims themselves, their families and the wider community. Although the Government finally admitted more could have been done to prevent people from losing their lives to drugs, we need to seek divisive action now. In this site, and as Douglas Ross said yesterday, the Scottish Conservatives have appealed for cross-party support to tackle drug deaths by opening up access to treatment and rehab programmes. Stemming from my right to recovery motion, we will be reaching out across parties in the chamber, and I am determined to help to build a consensus around new legislation that ensures that no one is denied the rehab support that they need. As has been mentioned before, the success of the vaccine roll-out means that we are more confident than ever that we can soon put this pandemic behind us. However, we must acknowledge that the peak of the mental health impact of the pandemic is still ahead of us, and so mental health support and treatment must be another top priority for this Government over this Parliament. The centre for mental health has recently estimated that across the UK a staggering 10 million people may need mental health support. Here in Scotland, the latest statistics suggest that up to a fifth of people in Scotland are waiting too long for mental health treatment. That picture is even more concerning for young people, as more than 1,000 children and young people have waited over a year to begin vital treatment. The Scottish Conservatives had called for the share of the health funding that is spent on mental health to be increased to 10 per cent by the end of this Parliament. However, as much as more funding will help, we also need practical steps to improve services and ultimately get better treatment for those who need support. To that end, we also suggested that there should be a permanent shift towards community mental health services by expanding programmes such as cognitive behavioural therapy, social prescribing and exercise referral schemes and also peer support. Presiding officer, in summing up, as a nation we have a significant challenge ahead of us and it is time, and time is quickly running out to act. From the NHS backlog to the mental health crisis, this Parliament must be 100 per cent focused on rebuilding Scotland. The differences in political opinion in this chamber are stark and we all know that. However, with the immense gravity of some of the challenges ahead, I believe that the best interests of the Scottish people will be served if we can co-operate in many of the areas that I have outlined this afternoon, and the Scottish Conservatives are ready to put recovery first. I now call on the cabinet secretary for health to wind up today's debate. I would be very grateful if you could take us up to around 10 to 5. Thank you very much. I welcome you to your role as well. I start off by saying how very grateful I am for the opportunity to close today's debate is the new cabinet secretary for health and social care and to listen to some phenomenal speeches, extraordinarily powerful speeches and very passionate speeches from new members in particular, and the old timers weren't too bad either. Let me say a word or two, because others have talked about their predecessors. Let me also pay tribute to the former cabinet secretary for health, Jeane Freeman. Many members have come up to me to say that they have very big shoes to fill. I am not convinced that I will be able to fill those shoes quite as Jeane Freeman did, but I will do my best to do as well as she did. History will judge her, I think, very kindly, as somebody who took the toughest of decisions and the toughest of times. Many people have said to me also from across the chamber, I do not envy you with the job that you have. That is true, but it also, as Annie Wells rightly reflected, is a huge honour, a huge honour to be the Cabinet Secretary for Health and Social Care at any time, let alone being entrusted with that responsibility during the most challenging of times. I will do my best, and I promise you to try this, and at times I am sure that I will falter, but I will do my best to work across party for the national interests that we are all focused on, and of course it is the focus of this very, very debate. Let me also start by doing, as the Deputy First Minister did, and passing on my deepest condolences to all those who have lost loved ones during this pandemic. This virus has touched every family, it has touched every community in Scotland. When we say that about passing on our condolences, it is because we should remind ourselves in the heat of debate, and there will be plenty of very challenging debate around this very issue of Covid recovery, that ultimately what we are doing is trying to pay the ultimate respect to those who have passed on, and that is to learn the lessons to make sure that we can do everything that we can to recover. Let me start also by referencing again those phenomenal first speeches by a number of members right across the chamber. I want to try to speak to as many of them as possible, but particularly those who ask questions of me in summing up. Let me welcome Gillian Mackay to the health portfolio. I look forward to working constructively with her. I thought that she made an excellent speech with a number of very good points, but she touched particularly on mental health support for NHS staff. That was a really, really important point for us to raise. I was at Monklands hospital yesterday, my first official visit, and I was delighted to meet the staff there. I was in the very good hands of senior nurse Karen Gowdy and many others at Monklands hospital. I want to thank them for the care and tension that they gave me during my visit, but every single person I spoke to, the nurses, the doctors, the consultant, the porter, the cleaning staff, every single one of them told me that it has been the most challenging, the most difficult 14 months of their lives. However, they all said to me that they were indebted to, as they described it, the NHS family that they had all pulled together. However, it is my responsibility and our collective responsibility to ensure that we do everything that we can to support their mental health. We are doing that with a mental wellbeing hub, but there is more that we can do and accept Gillian Mackay's challenge in that regard. She spoke also very well, and Mark Ruskell mentioned this in his summing up. A number of other members talked about the importance of the social care sector, and again, if any of us were ever in doubt of that importance and none of us should ever be so, then, of course, the last 14 months have challenged us all in that regard. Therefore, I am delighted to be working closely with Kevin Stewart, who will be the minister who will help to take forward our national care service and has already done a lot of work in the first week and the role in that regard. Of course, in our first 100 days, we will launch a consultation in relation to that national care service so that we can improve those terms and conditions. She also mentioned Gillian Mackay and her remarks about looking above and beyond CBT. She mentioned that CBT was very important. I can assure her that my wife, who is a councillor who deals with pleurism, also tells me that she has to look above and beyond CBT, too. So, as much as I get pressure on the chamber, I also get it at home, too. I speak to a number of other members. Neil Gray spoke again extraordinarily well. He has a seasoned politician, but his first contribution in this chamber. He asked me about close contact services when the guidance would be updated. It got updated yesterday, and I have sent him on the link while we were in the chamber. He is a good friend of mine. He is going to make an extraordinary contribution to this chamber, I have no doubt. Stephen Kerr spoke powerfully and asked me a number of questions. I was really interested to hear about his background. I was not in the Parliament when he made that contribution on behalf of his church. I did not know that he went from a preacher to a politician. Some might suggest that he has gone from a saint to a sinner. I would not do such a thing. The serious points that he raises and he questioned me. Again, I welcome that challenge. It was around vaccine roll-out, and a number of other members did as well. The reason why I am pushing as hard as possible to go as fast as possible is because JCVI guidance has changed from the second dose being administered from 12 weeks, which can now be administered from 8 weeks. We are pushing our health boards to go faster to schedule those appointments earlier on. We also have a good supply of AstraZeneca, which has not always been the case, because, as members will know, the guidance is not to use that for under-40s where possible, and therefore we have that supply available to hopefully increase the second doses to that cohort that is over the age of 40. On performance in relation to the NHS and its recovery, a number of members raised that and referenced the fact that I have said that it will take longer than weeks and months. I have to be honest about that. As health secretary, I can sit here and pretend to give a figure that I can pluck out of the air when I can tell you when we will have NHS performance not just at pre-Covid levels, but I want us to go even better than pre-Covid levels as a number of members have challenged me. However, I cannot pluck that figure out of the air. That is why the NHS recovery plan, which I hope will be a cross-party effort and can get cross-party endorsement, is important to publish in the first 100 days. It does not mean that in the first 100 days we will get that NHS recovery. I will do my best to push things as far and as hard as I possibly can, but I have already written to each of the health spokespeople to email them to ask them to come and meet them. I am sure that we will meet them very soon, and part of that conversation will be around the substantial part of that conversation and the remobilisation of the NHS. I turn to Pam Duncan Glancy. You are rightly getting plaudits from across the chamber because it was one of the, if not the best opening speech or first speech that I have ever heard from a member. You quoted John Smith extraordinarily well in terms of the opportunity to serve as Michael Marra. I cannot speak for him, but I know his family well, as I suspect you do, and I am sure that he would be very proud to see you and his family very proud to see you in this chamber. You are not just excellent in your own right very clearly, but there are many, many, many people who will look up to you as a role model. I was not the only one, I suspect, who had a lump in their throat and was about to shed a tear watching your interview at the Emirates when you were first introduced to Pam Duncan Glancy MSP. You will be a fighter, and I look forward to working with you. Maggie Chapman challenged us, challenged all of us in relation to the economy, and challenged us in relation to an economy that focuses on wellbeing, that focuses on human beings as person centres and people centres. I know Ben Macpherson and his role and the number of others who will be looking forward to working closely with you, as will I. I turn to Dr Sandish Gohani, who I have been impressed with right throughout my life. He and I were political opponents in Glasgow Pollock. I was impressed with him then, and I am even more impressed with him now that I think that he spoke very emotionally and very powerfully about his own role in the NHS, for which I thank him throughout the pandemic, but also extremely emotively about the challenges that he faces as a father in the NHS. That really struck a chord with me. I am, I say, a new father, two years old, but it seems like she was just born a moment ago. I cannot imagine not hugging my new-born daughter for eight weeks, so I commend you for the sacrifices that you have made, but also for the fact that, in your first and opening speech, you have said that you will be a champion for the NHS, and I look forward to working cross-party with Dr Gohani. Meghan Gallacher spoke very well on a number of issues, particularly about education. I look forward to having many discussions with you about health, but I am sure that my colleague Shirley-Anne Somerville will look forward to speaking with you about education. You asked about our education recovery plan. Again, my colleague Ms Somerville will, of course, give more detail of that in the debate next week, but it has already been said that, of course, we are putting a significant amount of money into education recovery, not just funding councils to increase teacher numbers by 1,000 and classroom assistance by 500. That is part of our commitment to 3,500 additional teachers. However, that summer programme, which so many people have rightly asked questions about, is hugely important to me. I am the stepfather or stepdaughter who is 12. She is in that transition between primary school and she will be going into high school. It has been really tough, because that is the year that you probably enjoy the most as a child of that age. She may lose some of her friends, if different friends go to different high schools, and she has really felt it. We can promise you that, of course, our focus will be on their educational attainment, of course, but also the other important aspects of life that young people have missed out on play, on socialising and so on and so forth. My colleague Shirley-Anne Somerville will give more details to that. I also commend Michelle Thomson, Michael Marra, Paul MacLennan and Collette Stevenson, for giving me all of their first speeches as well. In the remainder of the time that I have, I will try to address a couple of other issues that were raised. If I may, a number of people have rightly asked me about Glasgow. I say to Anna Sauer, who has spoken well this week about the challenges that Glasgow faces. He and I represent that city and the south side. Both our father's businesses have been in the south side and my father's business is still in the south side. It has been there for 40 years. We both went to the same school in Glasgow south side, too. We have a love and a desire to see that part of the city do well, but also the city as a whole come out of the current challenge that it is in. I can give him an absolute guarantee that, where there are those clusters in the south side of Glasgow in particular, they are getting our urgent and immediate focus. Vaccination in those hotspots has been prioritised for 18 to 29-year-olds. He asked about walk-ins for 18 to 29-year-olds. That is a very fair question and a very fair challenge. It is something again that is urgently being explored, but we have to be careful because where our priority will often be on the second doses because that gives you, for the current variant that we are dealing with, 88 per cent effectiveness. For one dose, you will only get 33 per cent effectiveness. For an older cohort that we know are more vulnerable and susceptible to severe illness, possibly today, there is a priority for that older cohort to get the second dosage for maximum protection. However, can we do both? Can we maximise the second dosage, as well as having walk-ins for 18 to 29-year-olds and the other cohorts below 40? I think that that is a fair challenge and I can promise him something that I am looking at. In terms of the do not attend, which a number of members have mentioned across the chamber, I have made it very clear to health boards right across Scotland that when they get towards the end of the day, if they have any leftover vaccine, my expectation is that they put immediate calls out, as the Hydro did a couple of weeks ago, to ask people to come down to get those dosages. However, there is a step before that, which is of course addressing why the do not attend is happening. That is what we are doing at the moment. Tayside health board have done a good power of work to try to understand that better, but I am happy to give way. Alex Cole-Hamilton I am very grateful to the cabinet secretary for giving away. I am sure that the chamber is very gratified to hear about the measures in Glasgow to deal with the hotspots there, but the hotspots and outbreaks of Covid-19 are not limited to Glasgow. As I said in my speech, Davidson's main primary was closed to my constituency on Tuesday. 11 classes are now self-isolating. There are dozens and dozens of infections there. He reassured my community that the Government's focus is very much with them and that they will be receiving due attention. John Swinney Yes, I am unconscious, so I am running short of time, but I was coming to Lothian after Glasgow. To say to Lothian that I spoke to the national clinical director Jason Leitch this morning about the situation in Lothian, he will have seen the case numbers, as I have seen. We have recruited two additional mobile testing units in Lothian. They are focused on where the clusters are. Davidson's main primary is that he mentioned, if he will forgive me, I will go away and take a look to see whether or not there are the appropriate testing facilities there. I will come back to the member and I am happy to engage with him directly in that regard. Craig Hoy On vaccines, will the cabinet secretary look to reports on today's East Lothian courier, which suggests that residents are routinely being sent to vaccination centres in middle Lothian and west Lothian, even when there is capacity in east Lothian? If that is due to a computer glitch, would the minister get this sorted soon before it impacts both a vaccine take-up and the number of young people that might come forward in the future? Cabinet Secretary for Health and Sport, I thank the member for raising the issue. I will take a look at that and I will see why that is the reason. I am conscious that I am very much out of time. We will be having a debate next week. In fact, our first debate next week is on the NHS and NHS recovery. I look forward to giving more details of what I intend to do in that regard. My absolute priority of this Government, not just my priority, but of this Government is responding to the immediate crisis of Covid, but also ensuring that the NHS is recovered and remobilises because we know—and I know, because I have some family members—I have a family member in particular who is waiting for an operation, but Covid then came, and I know the impact that is having on that individual. I am just one. I will end on this point where I started, which is that this has been an excellent debate. I am pleased that this has been the very first debate of this sixth session. I really look forward to working with all members, the new members, but those who are perhaps not so new either. As much as this will be our collective focus, we will have plenty of disagreements and heated arguments. Ultimately, the people of Scotland have entrusted us to work together in a period of time that none of us could have imagined. I am certain that not just the Government but every single one of us, regardless of party colours and stripes, tribalism or any other issues of ideology that separate us or divide us. Ultimately, on this issue, we will not let the people of Scotland down. Thank you. That concludes the debate on Covid-19. I am minded to accept a motion without notice to bring forward decision time to now. I invite the minister to move the motion. Thank you very much, Presiding Officer, and moved. Thank you. I will now put the question. The question is that decision time be brought forward to now. Are we all agreed? We are agreed, and as there are no questions to be put as a result of today's business, I close this meeting.


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Continuing with our qualitative study of the wave equation, today we are going to introduce two properties which we may say are exclusive to hyperbolic equations and hence in the second order equation that we are going to study namely wave equation, heat equation, Laplace equation. So these properties are exclusive to wave equation and they are known as domain of dependence and domain of influence. We will discuss more on that in this lecture. So the outline for today's lecture is first we start with defining what is domain of dependence and domain of influence and then in short I write DOD and DOI. So we find out what they are for one dimensional wave equation and then what they are for 2 and 3 dimensional wave equations. So Cauchy problem for homogeneous wave equation is given by this the wave operator or dialomb version equal to 0 that means we are considering homogeneous wave equation and this is the Cauchy data ux0 is phi x utx0 equal to psi x. So we have already solved this Cauchy problem in earlier lectures. So there are two questions on interrelationship between the Cauchy data and solution. So we are going to pose those questions now. In 1 let you be a solution to the Cauchy problem for homogeneous wave equation. Let x0 t0 be a point in rd cross 0 infinity sometimes we say x0 t0 is a space time point, point in the space time. Of course u of x0 t0 being the value of the solution at the point x0 t0 the Cauchy problem it would depend on the Cauchy data that is not a surprise. So now the question is does the solution depend on the values of phi x and psi x at every x in rd that is the question. If the answer was yes or maybe then we will not be devoting a lecture to this topic therefore answer is not going to be all x in rd. So there will be a specific domain in rd we will soon see that. So set of all x in rd on which the solution u of x0 t0 depends through Cauchy data is called domain of dependence for the solution at the point x0 t0. Let us move on to the second question. Let you be a solution to the Cauchy problem for homogeneous wave equation. Let x0 be a point in rd. The Cauchy data at x0 recall the Cauchy data phi and psi are defined for x in rd. So the Cauchy data at x0 namely phi x0 and psi x0 is expected to influence the solution. Now does the Cauchy data at x0 influence the solution u of xt at every xt in rd cross 0 infinity? The answer is set of all xt in rd cross 0 infinity such that the solution u of xt is influenced by the Cauchy data at the point x0 in rd is called domain of influence or region of influence of the point x0. So here once again answer is going to be not every xt in rd cross 0 infinity the Cauchy data x0 is going to influence. Remark on the two questions and their answers. The two questions could have been asked for non-homogeneous wave equation also. Answer would still depend only on the solution the Cauchy problem for homogeneous wave equation. Why is that the Cauchy data and the source term do not interact? Recall the formulas that we have derived for the solution of Cauchy problem to a non-homogeneous wave equation. So past and future cause and affect. These are the two points of view that we can present domain of dependence and influence. Question one let us rephrase it. Suppose I am standing at a point x0 at time t0 that is at the point x0 t0 in the space time. What is causing or responsible for the current state u of x0 t0 from the past situation or data at time t equal to 0? Question two rephrased suppose I am standing at a point x0 in rd at the initial time t equal to 0. What are the points x t in the space time at which the data or situation at x0 at time t equal to 0 that is at the current time or initial time influences or affects the future state u of x t. So cause and affect past and future dependence and influence. Rest of this lecture is devoted to determine the domain of dependence and domain or region of influence for Cauchy problems for the wave equation in d space dimensions d equal to 1 to 3. The explicit formulae for solutions to Cauchy problems namely the Alambert formulae for d equal to 1, Fossum Kirchhoff formulae for d equal to 2 and 3 they will be used the formulae will be used. So let us move on to one dimensional wave equation and find out what is the domain of dependence. The Alambert formulae for the solution to Cauchy problem is given by u of x0 t0 equal to phi of x0 minus ct0 plus phi of x0 plus ct0 by 2 plus 1 by 2c integral x0 minus ct0 to x0 plus ct0 psi of s ds. So to compute the solution at the point x0 t0 what we need is the values of phi are needed exactly at two points x0 minus ct0 x0 plus ct0 and the value of psi are needed psi appears here it is an integral on the interval x0 minus ct0 to x0 plus ct0. Therefore the domain of dependence is the interval x0 minus ct0 comma x0 plus ct0 this is the interval which is the domain of dependence for the solution at the point x0 t0. So this is the picture here we have the point x0 t0 this is the interval on the x axis x0 minus ct0 x0 plus ct0. If you notice x0 minus ct0 is nothing but the line through x0 t0 the characteristic line given by x minus ct equal to x0 minus ct0 where it touches the x axis is precisely x0 minus ct0 comma 0 we are not writing that we just write x0 minus ct0. Similarly x0 plus ct0 is the point of intersection of this x axis and this characteristic x plus ct equal to x0 plus ct0. So this is the interval on the x axis on which the value of the solution at x0 t0 depends. So the solution at x0 t0 depends only on the Cauchy data from the interval x0 minus ct0 comma x0 plus ct0 what do we mean by this suppose I take two sets of Cauchy data phi psi and phi 1 psi 1 so that they agree on this interval x0 minus ct0 comma x0 plus ct0 that is phi is identically equal to phi 1 psi is identically equal to psi 1 on this interval. Let u1 u1 denote the solutions to the Cauchy problems for the wave equation with this Cauchy data phi psi and phi 1 psi 1 respectively then u of x0 t0 is equal to u1 of x0 t0. In fact u of xt is equal to u1 of xt for every xt in the triangular region determined by the two characteristic lines through the point x0 t0 on the x axis. For example, this is the point x0 t0 this is x0 minus ct0 this is x0 plus ct0 suppose I take a point which is inside somewhere here of course we know the value at this point will depend on this interval's value but on this interval phi and psi are equal therefore this holds for any arbitrary point that you take the solution will be the same with both the Cauchy data it is not going to change. So this is the domain of dependence picture once again x0 minus ct0 x0 plus ct0 so I have already demonstrated suppose I take a point here then the solution at that point depends on the values of the Cauchy data on this interval. So if you take a point here these are the characteristics passing through this point and where it touches on that is on this. So therefore if the Cauchy data phi psi and phi 1 psi 1 are coinciding on this interval then the solution will be same for both the Cauchy data that is u and u1 coincide on this triangular region. In particular changing the Cauchy data outside the interval x0 minus ct0 x0 plus ct0 has no effect on the solution at the point x0 t0 because the solution at x0 t0 depends only on the values of phi and psi in this interval therefore if you change it outside does not matter that was what was proved by considering the two Cauchy data that we considered phi psi and phi 1 psi 1 which are agreeing on the interval x0 minus ct0 x0 plus ct0 therefore solution is the same at x0 t0 outside this interval phi psi may not be same as phi 1 psi 1 that does not play any role at all. So that is the effect of change in initial data is not felt at the point x0 for all times t less than or equal to t0. Let us have a look at it again so this is the point x0 t0 what does it mean this is the point x0 this is x0 minus ct0 x0 plus ct0. Suppose I am standing at the point x0 this is a t direction right t direction suppose I am standing at some time t equal to capital T then I am at this point at this point solution is here right depends only on this interval. So up to this time it will depend only on the values here suppose you cross this time and stand here then yes this part will be new right this piece this this part will be new and here phi equal to phi 1 psi equal to psi 1 but here phi may not be equal to phi 1 may not be true okay. So therefore the solution at this point u of x let us call this point as x0, t1 so u of x0, t1 may not be same as u1 of x0, t1 because in this piece and in this piece phi and psi we have no information whether they coincide or not. So thus we may say that the solution at x0 t0 has a domain of dependence given by this interval. So let us look at the domain of influence of a point x0 on the x axis it is this set xt in r cross 0 infinity such that the domain of dependence of solution at xt contains the point x0. So what is that suppose this is my x this is my t directions suppose I am a point x0 now what is the domain of influence of x0 it contains those points xt such that the its domain of dependence contains the point x0. Let us consider a few points and see let us take a point p the solution at this point will depend on this interval and this is the domain of dependence for p it does not contain x0 therefore this p does not belong to domain of influence of x0 for example I am at this point in space time. Now the domain of dependence for this new point q is this interval and x0 falls inside that therefore q belongs to the domain of influence of x0. Let us consider one more point suppose I am here r the solution at this point this is the domain of dependence for r of course x0 is not there in it therefore r does not belong to domain of influence of x0. Suppose I take another point here at this point if you notice in the domain of dependence for this point yes x0 belongs to so therefore x0 influences the solution at s so s belongs to the domain of influence of x0. So since the domain of dependence of solution at xt is this interval x-ct x plus ct the domain of influence of x0 is this set let us look at this picture here okay if I take a point here of course x0 will lie in the domain of dependence for this point okay whereas if I take a point outside this v shape region definitely no okay. Similarly imagine this is r exactly same problem I have already written dots here the domain of dependence for r is this interval and x0 is not in that interval. So any point which is outside the v shape region x0 will not belong to the its domain of dependence and on the other hand any point inside this v in this region x0 will belong to the domain of dependence for solution at the points in this region domain of influence of an interval we have considered domain of dependence of a point now we are going to consider domain of influence for the interval how do we define that let us take an interval on the x-axis domain of influence of this interval should be the union of domain of influences of the points of the interval ab. Thus domain of influence of the interval ab turns out to be the set of all those points xt such that the domain of dependence of the solution at xt has a non-empty intersection with ab. So let us draw this line and take a piece here ab this is our interval now let us find out certain things for example I am at a point here okay. So at this point this is the domain of dependence for this point p and it does not intersect with ab so therefore p does not belong to domain of influence of the interval ab for example I take another point at this place let us call it q here this is the domain of dependence for q and it intersects this interval ab therefore the point q belongs to the domain of influence of the interval ab. Now the region which is given here is nothing but this this is x minus ct equal to b this is x plus ct equal to a. So if you take any point in this tub shaped region let us say here then definitely the domain of dependence will intersect ab for this point r and if you take a point here let us call it s then also it is going to intersect the interval ab the domain of dependence of that. So therefore the domain of influence of the interval is this particular set yeah. So here once again we have this picture if you take a point here this is the domain of dependence for p it is not intersecting ab if this is a point q the domain of dependence is here not intersecting on the other hand if you take a point here r then it is going to intersect it is much bigger than ab but definitely intersects ab and if I take a point here this is s then like that still intersecting. So if this is precisely the domain of influence of the region ab let phi psi b supported in this interval ab I am taking such a data that means phi and psi are 0 outside this interval ab. So this side phi and psi are 0 this side phi and psi are 0 for each fixed t positive where is the support of x going to u of x t. So let us fix time so this is the time right so this t equal to some capital time t. Now if you notice a point here ab will not influence this point p or any point which is to the left side of this particular line it will not influence therefore solution is 0 and similarly to the right side of this line to this side if you take any point q u at q is also 0 therefore only on this really it may be non-zero. So therefore the support is contained in this interval what is this point and what is this point that you can check it is going to be an interval actually this is a a has moved this side by time t we are going to see you can compute and see a minus ct similarly b has moved this side to this point this is b plus ct this is a minus ct the support will be contained in this. So support might increase of course you see original ab is the support for phi and psi and now the support is here for the solution at the time t equal to t it might increase but notice support is still compact. The support of a and support of phi and psi is inside ab it means it is a compact set support is a compact set now the support is inside this interval it means this function has compact support that is an interesting observation about the propagation of the initial disturbances. Let us look at the two-dimensional wave equation and domains of dependence and influence for them this is a formula for the Poisson kickoff formula for the solution of the Cauchy problem for the wave equation in 2D. Now if you notice the formula depends the values of phi and psi only on this disc therefore the domain of dependence for the solution at the space time point x1 x2 comma t is this disc of radius ct with center x1 x2 one may also consider closed discs that is not a problem because it is an integration right it is an integration so the boundary what is the difference between the closed disc and the open disc it is a boundary and that does not make any change to this integral it does not affect the integral so there is no plus here there is a problem okay fine okay so if you want it to be a closed set if you want it to be a closed set but there is no need for asking that so we do not take this point of view now what is the domain of influence that is given by set of all space time points such that distance between x1 x2 and y1 y2 is less than ct okay the y1 y2 x1 x2 distance is less than ct that is a domain of influence please convince yourself about this answer everything comes from this formula so this is a set of all those points which can be reached within time t from y what is this this is the distance between the boldface x and boldface y that is less than ct okay if you divide distance with c so distance by speed is less than this t so that means you reach within within the time t from y to x or x to y so three dimensional wave equation what are the domains of dependence and influence this is the formula Poisson Kirchhoff formula s of x comma ct is the sphere so therefore the domain of dependence is s of x ct because that is where the integrals are on right and domain of influence at the point y in rd is now norm x minus y equal to ct because of this sphere earlier it was a disc that is why it was less than t now this sphere therefore distance is precisely ct in other words those points which can be reached those points x which can be reached exactly at time t from the point y let us summarize we introduce the dual concepts of domains of dependence and influence like past and future like cause and effect extending the concepts of domains of dependence and influence for IVVP is straightforward domains of dependence and influence were computed explicitly explicit formula for the solutions were used in lecture 5.3 we will arrive at the same conclusions without using the explicit formula for solutions but of course you have to use something thank you.