Wel i'n hwn, dda, ac wedi cael ei wneud ar gweithio'r gweithio'r gwaith ffordd, yw'r gelweddau hynny o'r tîmbydd y ffordd a ddechrau'r dddangos. Ar ddiweddau, eu hwnnw'n fawr yn gweithio yw'r newid yw'r gweithio'r gweithio'r gweithio'r gweithio'r gweithio'r gweithio. Felly, mae'n cael ei chweithio'r gweithio'r gweithio'r gweithio'r gweithio'r gweithio'r gweithio. As you will have heard over the last few days, a new mutated strain of coronavirus has been identified. It is much more infectious and it is moving quickly in Wales. I'm joined this afternoon by Dr Chris Jones Wales's Deputy Chief Medical Officer, and he will now explain more about this new strain of the virus. Chris. Thank you, First Minister. The first thing to say is that all viruses can and do change. Genetic mutations are a natural phenomenon of viruses, and the coronavirus is no different. We've seen a number of mutations since the SARS-CoV-2 virus was first identified in Wuhan just over a year ago, and most of these mutations turn out to have no significance. But this new strain of the coronavirus, which has been detected in the UK and to other countries, is concerning. We are mainly seeing it in London and the south-east of England, but also in Wales. The way the virus has spread rapidly in these areas is very similar. This new strain appears to be much more infectious than the strain which originated in Wuhan, and is much more easily transmitted from person to person. At this stage, we do not believe that it causes a more serious illness than what we already understand, and we do not believe that it will affect how the vaccine works. But we will continue to closely monitor this new variant and what the scientific evidence is telling us. On Monday of last week, we were aware of 10 cases in Wales. By Friday, this had risen to 20, mainly around Bridgend and the Vale of Glamorgan. But a new analysis by the weekend suggested this new strain is much more common and is present all over Wales. This includes north Wales, even though overall rates of the virus are lower than they are in south Wales. The Office for National Statistics over the weekend published data from its infection survey that shows the new strain was present in 28% of samples from Wales in the second week of December, more than double the number in the previous week. Public Health Wales colleagues advise us that they feel this new strain could be causing up to 60% of coronavirus infections in Wales. This new variant looks very likely to be the significant driver of the huge growth in cases we have seen in Wales in recent weeks. I will now hand back to the First Minister, but I would be happy to take questions later. Chris, thank you very much. So, here in Wales, the pandemic changed gear in late November, quickly eroding the gains which we had made from the firebreak and causing this huge increase in cases and hospitalisations. And as you heard just then from Dr Jones, we now have a better understanding of why that has happened. At the end of November, the seven-day coronavirus rate for Wales was 232 cases per 100,000 in the population. Today, it is almost three times that number at 623 and rising. A month ago, there were just under 1,700 people with coronavirus symptoms in our hospitals. Today, there are more than 2,300 and again that number is rising. Our critical care units are operating beyond their normal capacity and our NHS and frontline staff are certainly stretched to the limit. Very sadly, over this weekend alone, Public Health Wales has reported more than 100 deaths. And as we enter the Christmas period, I hope we will pause just for a moment to think of those 100 families but the over 3,000 families here in Wales for whom this Christmas will never be the same because of loved ones taken away from them by this cruel disease. Unless we can regain the grip of the spread of coronavirus, we will undoubtedly see more deaths here in Wales. And if we continue to see the case rise go on unchecked fuelled by this new highly infectious variant of the virus, the effect on our NHS will be profound. We must do everything we can to prevent that from happening. On Saturday, I took part in an urgent meeting with the Scottish and Northern Irish First Ministers and with Michael Goh from the UK Government and with the most senior clinical and scientific advisers. There we receive new and worrying information about how widespread this new strain of the virus has become and how quickly it is moving. During Saturday afternoon, the Welsh Cabinet met, we received further information about the spread of the new variant strain here in Wales and about the significant pressure it is causing in all parts of the NHS. As a result, we took unavoidable and immediate action to bring forward the alert level four restrictions and to change the Christmas arrangements because of this incredibly serious turn that the pandemic has taken here in Wales. Of course, I wish that we had been able to give everyone more notice of these changes, but in the light of the information that we had in front of us, it was imperative to take swift action to prevent further harm and to save lives here in Wales. Now, because of the impact on businesses, we've extended the restrictions business fund by an extra £110 million. That's £270 million for companies affected by the alert level three and four restrictions and, over and above that, an extra £180 million fund for hospitality and supply chain businesses. Once again, I want you to know that our local authorities are working incredibly hard to get that financial support to businesses as quickly as possible. I'm able to say today that if the UK government provides support to businesses in London and the southeast, which have also have to close, then we will pass all the additional funding we get here in Wales as a result onto our own businesses. Unlike previous lockdowns, all retailers will be able to offer click and collect services even as non-essential retail is now closed. While 2020 has been an extraordinary year and a very difficult one for us all, this is a pandemic that has been full of surprises and it's taken another deeply unpleasant term just as we were preparing to celebrate Christmas. This new strain is a challenge for us all, but it is another challenge that we will manage together. Together we have come through so much this year from those very early days at the start of the pandemic when we were just learning about the virus to the long summer days when the coronavirus appeared to be in retreat. Since then, these have been challenging weeks, but throughout them all, our greatest strength in Wales has been the way in which people here have responded to the virus, working together in social solidarity to keep each other safe. For so many months we have followed so many rules, kept the two meter distance, washed our hands, worn a face mask. Now we all need to redouble those efforts in the face of this new strain of the virus. If we keep ourselves and our loved ones safe, there is a better 2021 ahead of us. A vaccine which offers us the hope of a different relationship with this virus and hopefully another vaccine soon around the corner. Diolch o galon i chi gyd anodolau clawen o'r cwrs i bawb. So for the last time this year we'll take questions and as ever, all the answers will be broadcast live on our own social media channels. First today, we'll go to Teleri Glyn Jones at BBC Wales. Diolch am yr iawn to you both. You've outlined how the situation changed over the weekend dramatically, but was the writing not on the wall when it comes to the seriousness of the situation? We already knew that there was a new variant. The cases in the south Wales were already high and were rising, and the medical profession had intervened last week calling for you not to relax the Christmas, the rules over Christmas. First Minister, you appreciate it's a very difficult decision for you to make, but do you regret making that decision at such a late stage and to the DCMO was the scientific evidence not already there to make a decision before this weekend? Well, Teleri, I've come to these press conferences regularly over the last fortnight having to announce further restrictions on life here in Wales, whether it was the closure of parts of hospitality, whether it was the way which school terms ended and on Wednesday of last week I announced a level four lockdown here in Wales immediately after Christmas. So I don't think it would be a fair thing to say at all that we have been slow to act. We have acted in response to the views of clinicians in response to the rising cases. What was different this weekend was that we had a new explanation for why we are seeing the rate of increase here in Wales. This new variant with its transmissibility, the speed with which it spreads and that's why we had to bring forward our plans for a tier four set of restrictions across Wales from the immediate post Christmas period to the weekend and I think at every stage we have done our best to follow the science to act on that advice and that's what we were doing on Saturday. In response to your question to me, it is clear that the public health situation in Wales has been a cause of concern for some weeks despite the restrictions that are in place but the issue of the new virus variant is very very recent indeed. We only need to know about such variants when they sort of take off and demonstrate their competitive success against the previous versions of the virus and that only became clear at the end of last week. Over 60% of cases in London are now due to this virus variant and I think once you know that you know that this is a highly transmissible agent and that it will just take off and our figures will just get worse unless you take immediate action and that clearly happened over the weekend. Ylch yn ddweud i'r Ffyrdd Minister. Some of our key workers, those that we clapped for earlier in the pandemic will be working on Christmas Day. Are you considering making an exception in the rule for those who are already sacrificing their Christmas to work and so they too can spend time with their families? Well thank you Tyn, you're absolutely right of course. There will be people who will be working on this Christmas Day to allow the rest of us to be able to have that day to be with a small number of other members of our family. We are discussing with the TUC and others whether it would be possible to offer those people who are working on that day any compensatory arrangements. They're reasonably complicated in a practical sense but I can assure you we are discussing them here in the Welsh Government and in response to views put to us by the Wales TUC. Okay over to James Crichton Smith at ITV Wales. Thank you First Minister. My first question is to the DCMO. How long have you been advising that a lockdown over Christmas was needed? All we can do is to talk about the public health situation and discuss that with ministers and ministers have been kept very well informed about that. With regard to the virus variant we learnt about the variant on Monday through a chief medical officer's call and briefed the minister but at that stage we just had 10 cases in Wales. We briefed the health minister again on Friday when we knew we had 20 cases and it's only really over the weekend following a nerve tag risk assessment on Friday that actually and the further analysis in Wales that we realised that this virus variant is potentially driving our increasing our rate. I'll come on to my second question shortly but no no I think there's two questions please. Is this your second question? I wanted to get clarity on when advice on... Well you will know that because... My second question my second question First Minister is what are the real numbers as far as how many people in Wales have got this variant? What are the impact on the modelling? Apologies you know I may just have missed the very end of the question. What impact so what are the numbers regarding this new variant so how many cases are there in Wales with it and what impact are those numbers having on the... Thank you very much. I think I've got that and apologies in relation to your first question just to say as you will know the chief medical officer publishes every time we introduce a rule change in Wales. His own statement that we publish and that that will demonstrate the advice that the Welsh Government has had at every stage from our chief medical officer. The figures that we have at the moment that we know of are over 600 cases of the new variant in Wales but that is almost certainly as our public health colleagues tell us a significant underestimation because only a proportion of Welsh tests go to the Lighthouse Laboratories currently able to detect it. So we expect those numbers to be well below the numbers that are actually in circulation. In terms of the modelling we ask our colleagues at Swansea University who provide all reasonable worst case scenario modelling to keep it up to date for us and we will be making sure that they have this information so that they can provide us with a further iteration of the model to give us a sense of where this new variant might take us because of the way it is increasingly infectious and well then we'll be using that for our planning purposes as we have all along. Thank you very much over to Will Haywood at Wales Online. Thank you First Minister. I think this question will work for both of you if I may. Given that this new strain is spreading quicker how has that affected your modelling and can you give a statement on how this is going to affect the reopening of schools? Will schools be going back at the same time as before and when they do go back will they be running the same way as they were before giving how much easier it seems this virus can spread? Well on the modelling front well we will be passing this information to the people who do the modelling. For us you know we've relied on a model developed by academic colleagues here in the university in Swansea and we will ask them to give us their latest estimations of how a virus that circulates at this speed will drive the numbers over the next few weeks. The key thing is as we've both been saying all through the conferences is that the actions we have taken and the things we all need to do will be the most effective ways of bringing those numbers down and the Swansea modelers will take into effect the fact that the tier four arrangements in Wales came into effect over the weekend. On the schools issue we reached an agreement last week with the local education authorities for a phased return after the Christmas break a period in which schools will be able to adapt to these developing circumstances where individual head teachers will be able to take into account the particular circumstances in their schools. A fortnight is a long time in the progress of this virus and of course we will continue to discuss with our education colleagues in the trade unions the developing picture over the next couple of weeks but the fact that we've got agreed flexibility for those two weeks I think means we've already got a sound basis for how schools can be reintroduced and our young people can resume their education in the post-Christmas period. Just to comment further on the modelling assumptions at present we believe this virus variant is perhaps 70% more transmissible than the previous virus and that if it became the dominant virus variant it could increase the r value by 0.4. Now at the moment we don't necessarily think it is the dominant variant but that would have to be factored into modelling and as the First Minister says that modelling would also need to factor in the impact of the actions that have been taken over the weekend bearing in mind that there were pre-existing restrictions in place on household mixing and then those models are used to we translate those into the impact on the NHS into likely numbers of beds required and ultimately deaths. On school so just to declare it's there's no immediate plans for a change but you're not rolling anything out over the next two weeks as more information comes out is that fair? Yeah I think it's fair in the sense we'd already agreed a flexible return we'll now have to see how much that flexibility needs to be exercised and we'll do that with our partners in the education field. Okay on testing if I may we've had several reports of testing coming under great strain with five-day turnarounds not uncommon several services have told us that several of the lighthouse labs in the network are close to being totally overwhelmed and why are there such delays on tests again and what are you doing about it given that the issues in the lighthouse labs have been on and off since September? Well those are not the figures that I have seen Will the last figures I saw were that around 90% of tests that required a one-day turn around were still getting a one-day turn around. There has been a huge further surge in the number of people coming forward for testing and that is bound to put the system under strain but we had appeared as you said earlier in the autumn when the numbers were not where we wanted them to be for four or five weeks in a row they had recovered strongly recovered primarily because the lighthouse labs were operating far more effectively and we've had 90% of tests being returned within a day for a number of weeks now you know I can't say that given what has happened over the weekend and the anxiety that that will cause for people bringing more people forward for testing that the system won't be under strain but the system has been working well and it's because of the success of the lighthouse labs that we've achieved those figures and I think we should give some recognition to the hard work that's gone into making all that happen. Thank you First Minister. Thanks very much Will over to Dan Bevan at LBC. Thank you First Minister and Dr Jones good afternoon see you both First Minister first question to you if I don't mind. Since we're already running past the reasonable worst case scenario I understand there hasn't been a new one since this new strain has been discovered and also that lockdowns tend to take about three weeks as you've told us previously to show effect in hospital surely it would be a good time to let business owners know that realistically it might not be possible for them to open in three weeks time. Well putting the way that you put it Dan I'm happy to echo that it might not be possible well I can't say to them and wouldn't be right to say to them is that there is no possibility that things could could be amended at the end of three weeks so I think anybody looking at the figures anybody hearing what has happened over the weekend will know that there are difficult weeks ahead and I'm sure people in the business community will be factoring that into their own planning we will as ever continue to stay close with them sharing the information that we have with them but it is right to have a review the restrictions in England are being reviewed after two weeks we will review after three and if there are any possibilities to mitigate some of the impacts from tier four restrictions then we will want to see what we can do but it is might it be as you put it that further restrictions will be necessary beyond three weeks I'm afraid the answer to that of course has to be yes. Thank you and if I could extend this question to the both of you considering that Christmas is a difficult time of year for people who suffer loneliness and mental health issues what modelling was done to assess the impact that this is clearly going to have this lockdown over the festive period that's clearly going to increase the chances of those things having a negative effect on the general population and how much is that brought into your discussions when you're talking about whether level four needed to be restricted and brought in art. Well whenever we consider taking further action we are always balancing the four harms that come from coronavirus and you know I've been here at this podium a couple of times recently talking about the impact on people's sense of mental health and well-being from the restrictions particularly over Christmas so we are always having to try and find the right balance between the urgent need to take account of the impact on people's physical health alongside the impact that we know the restrictions have it was very actively discussed by the cabinet on Saturday afternoon we knew by then uh well we believed we knew by then that in England there would be no mitigation at all over the Christmas period uh and we decided still to allow that one day I know it's only a very brief 24 hours but that one day can still be very important to people who are lonely who are isolated and have at least something that they know they can do here in Wales and it also drove our decision to continue to allow a single person household to be able to be part of an extended household with one other household during the level four alert period and all of that was our response to exactly the points that you are raising Dan I don't have very much to add to what the First Minister just said other than to say that the models do include an effect related to Christmas recognising increased social mixing. Diolch gus. Darllianne Hale at PA. Good afternoon to both First Minister you said that we know the better understanding of why there's been a surge of cases of course as it has been said previously the effects were already clear when we were due to have the relaxed Christmas periods can you explain to us how does knowing why there's been a surging case surging case changed the picture for you considering you already knew there was surging cases well I think it's exactly that that you know we have a cause and now uh well we have the effect we knew the effect we could see it in the numbers and now we have a better sense of the cause when you have a better sense of the cause you have a better sense of what actions you need to take and how quickly you need to take them so this is a virus which causes a much faster circulation of the virus means that you are more likely to catch it that if you have it you may you may be more infectious to other people and therefore the need to take every action as quickly as possible to begin to prevent that from happening is what drove our decision making on Saturday so you're right we we were already seeing uh the impact of rising numbers when we had a better insight into why that was happening it drove the decisions that we made thank you um there will be many people who are working on Christmas day obviously people working in the NHS including them as well they'll will have plans of met family members on other days perhaps Christmas eve a boxing day will you be allowing people to choose which 24 hours they can meet with others if they are able to on Christmas itself I think I said in answering well Hayward's earlier question that this has been raised uh with me by the Wales uh TUC and of course we recognise the fact that there will be many people who have to give up their Christmas day uh and in this unique year that means they'll be missing out on arrangements that other people are able to make so we will discuss it uh with the trade unions and other public sector partners to see if there is anything that can be done but I just repeat what I said to Will really uh it's more complex than it sounds and we'll if we are able to do something it'll have to be a solution that is workable and deliverable uh go to Steve Bagnell of the Daily Post please thank you First Minister um we've heard the new variants has been detected in north Wales is there any more information in what parts if there are concentrations in certain areas and how widespread may it be across the region I might ask uh Dr Jones to lead off on that and I'll tell me if there's anything I can use fully out I can provide a partial answer over the weekend public health Wales colleagues were able to undertake an analysis of the samples from Wales that have gone to lighthouse labs that can recognise this variant that amounted to about 6 000 in total of around 42 000 cases from earlier this month in Wales and of the north Wales samples 22 percent demonstrated the variant now that that is not to say that um that is the prevalence now because I think as we're indicating this is increasing but it does provide some sort of indication and that that's consistent with the ons estimate of between 20 and 30 percent early in December but I don't have any figures about where in north Wales those samples came from thank you and uh with the new variants and obviously you've introduced a lockdown to counteract the recent rise of COVID-19 how concerned are you now about its impact on the NHS and the possibility that being overwhelmed in the coming weeks well I think we've been concerned for a number of weeks as we've seen these numbers growing and as you heard earlier you know we heard directly from frontline clinicians last week about the impact that they were concerned about not necessarily in the here and now but in the middle of January if these numbers were to continue to rise and coincide with the normal winter pressures that the NHS always has to face in the month of January so what the information at the weekend did was simply to provide a new urgency to the need to take action to prevent that impact not today and not next week going for a difficult couple of weeks we know but as we move into January when other pressures will be at the height we'll now be mitigating the impact of this virus and the new variant of it so it was exactly because of those frontline pressures the bed numbers that we are seeing the critical care impact that we are seeing that lay behind the actions we'd already taken and now this new variant accelerating the need to take those actions precisely in order to defend the NHS and to save people's lives Steve thank you very much to Thomas Moody of the South Wales Argus we've seen in England that people are being given refunds for training coach journeys that they booked for the five day Christmas period that they now can't use. Do you think they're doing something in similar here in Wales? Yes Thomas thank you so Transport for Wales which is the part of the Transport Network in Wales that we most directly have accountability for has already said that it will be offering refunds. We are seeking some urgent clarification from the Treasury as to where the funding is coming from for the promise that's been made in England I've had to say a number of times here that the Treasury needs to understand that it is a Treasury for the whole of the United Kingdom not simply the Treasury for the UK Government and if money is being supplied in order to be able to recompense people in England then the consequence of that must be felt in our budget so that we can do the same. Thank you and based on Will's earlier question about testing can you give us an update on the test trace protect scheme as well what's the standard period at the moment for people being contacted and what percentage of contacts are being reached? From memory Tom I think last week the figures were that 85% of index cases as they called it the first case were being contacted and I think 81% of all their contacts were being contacted as well. I don't have in my head the length of time that all that was taking but just as the testing system is under pressure from more people coming forward for testing so the TTP system is then under pressure because that means there are more people who need to be contacted and some of the timeliness of that has an impact as well but as of last week despite the rising numbers the percentage of people being contacted by our TTP system was still holding up and the actions will be of taking in terms of going into an early lockdown will feed through reasonably rapidly into the TTP system as well. We saw that in the fire break where the action to the fire break had an impact on reducing numbers of people needing to be contacted through TTP so we will have seen some relief in that system as well. Thomas thank you very much over to Rob Taylor at Drexham.com. Good afternoon the DCF Mo you said earlier that you only need to know about such variants when the figures take off and those figures came out at the end of last week. In the UK briefing on Saturday it was said by Patrick Balans that by the middle of November about 28% or so cases in London and the south east of England reduced the new variants and by the week commencing the 9th of December figures were much higher and in London over 60% more cases of the new variant. Is that gap due to lack of information supply from the UK Government and First Minister does that indicate that Wales needs to impact people deeper in the information supply meetings that are taking place in England? We are fortunate in the UK to have the Genomics UK Consortium which is a collaborative effort to undertake surveillance of different gene sequenced viruses circulating and that mechanism is operating all the time and Wales is a significant contributor of samples to that system. Variants come and go all the time. When the CMOs updated Frank Atherton on Monday I think there was a suggestion that this virus was more transmissible than the previous virus variant but that was still with low confidence but that situation clearly changed. NERVTAC undertook sequential risk assessments last week and it was only after they met on Friday that they said that this is now becoming the dominant virus variant. So at the time when the emergence of this variant as a very significant contributor to increasing case rates in London and the South East became apparent then that information was shared with us. Sir Rob, I don't think we know any less in Wales because anything was being kept from us. What we've learnt and I'm sure you've heard as well is that it's only two of the Lighthouse labs that the test they use happens to pick up this variant. So how much you know about a local population depends very much on how many tests from any one locality happened to be going to those two labs. So one of the reasons why we know a fair bit about North Wales is that quite a lot of the tests from North Wales go to the Birmingham lab which is one of the two labs able to detect this variation. From South Wales far fewer tests proportionately have gone to the Milton Keynes lab which is the second lab that offers it to it. So I don't think it's because anything has been kept from us. I think it is simply you know just a matter of how many tests end up going to one of the two labs able to identify it. Here in Wales as Dr Johnson said we've had we have our own genomic sequencing capacity. I think I'm right in saying that the United States has done the most genomic sequencing England has done the next most and Wales is the third in the world in the amount of genomic sequencing that we have been able to carry out and some of those very early numbers came to us not because of Lighthouse lab capacity but because of things that were being picked up through our own genomic sequencing. The amount of initial vaccine supply for the entire of North Wales appears to have equated to one or two or even three boxes of the 975 units of vaccine. Frontline staff in hospitals, frontline staff in care homes and some residents have had that supply but there doesn't appear to be much depth or growth in those programmes. Is the volume going to increase sharply and does North Wales really only have 12% of the priority population in Wales? Well you can be sure North Wales has absolutely its population share of the vaccine we have and Wales has a population share of the UK supply so whatever comes into the UK we get our fair share and then we try and make sure that every part of Wales has its fair share as well and as you will know some of the pioneering work that's been done in relation to care home visiting has been happening in North Wales in a way that hasn't been available elsewhere. We are dependent on complex supply chains of the UK government has the lead in in making sure the vaccine does come into the United Kingdom you'll have heard some reports overnight of some military preparation to make sure that if other routes into the UK are temporarily suspended because of the new variant it will still be possible to fly into Wales. Supplies of the Pfizer vaccine from Belgium. We remain hopeful I mustn't overstate it that the Oxford vaccine will get regulatory approval soon and then we will have more rapid numbers available including the work that is being done in rexham to supply what will then be the whole of the United Kingdom. Over to Nathan, Nathan Schu Smith at the speaker. Thank you, good afternoon to you both. First year question to you DCMO. Is increased testing going to be any more important with this new strain and would you encourage or discourage people from getting tested right now or is it simply more important for everyone to assume that they have the virus as has been suggested by some ministers in the UK government and just be really careful to forward that preventative measures? No, I think the knowledge of the increasing prevalence of this virus variant has been really important for us because we can now have a better understanding of what the risk is that we face and therefore the actions that need to be taken. But knowing about this virus variant doesn't fundamentally alter the way we need to manage this pandemic situation. We do need to ensure that there are samples being sent on a regular basis to labs that can measure it so we can track its progress within Wales and its contribution to the pandemic. But overall it doesn't alter any of the public advice about how to protect yourself. Social distancing, hand hygiene, respiratory hygiene as well. All of these measures are the same but just required to a much more rigorous extent. Question to you First Minister, if I may. How much concern do you think there should be over the temporary travel bans that we've seen over the last day or so? And how closely are you in conversation with the UK government about the effects that they may have and how they may be resolved? Well I think they are a sign of the seriousness with which the rest of the world is taking the emergence of this variant. We are drawing on our Brexit preparation here to make sure that if there are temporary impacts at ports and so on, that we can use the planning we've all ready done for what may happen in January. We do have regular contact with the UK government. We are anticipating a Cobra meeting not yet confirmed this afternoon and if that does happen there will be a further opportunity then to make sure that we are learning from developments for which others are responsible but contributing our own information about the developing position here in Wales. I don't think people should take more from this than is warranted. These are immediate reactions to a fast developing situation and governments around the world will be looking to make sure that they have equally rapid resolutions. Thank you Nathan, over to Tom Magner at Carersworld. Each of my two questions has got a political and the medical element so I'll leave you to decide which part you answer. The first question is about this significant mutant strain. Higher transmissibility must mean higher risk to the vulnerable and to unpaid carers where the health of two people is potentially at risk. Our viewers would particularly like to know whether or not asymptomatic people are showing this new strain and are people who've tested positive for coronavirus being told they've got the new strain, if not why not and could you summarise generally your concerns for the future political decision making and planning for vulnerable groups particularly given that it is only two labs can detect this variation? I'll probably ask Christopher first and then I'll tell me on the very last one. We don't know for certain that asymptomatic people will demonstrate this variant but there is absolutely no reason to think that they would not. At the moment the evidence is that the illness created by this virus variant is indistinguishable from the previous COVID-19 illness that we recognise so I would assume that people would be just as likely to be asymptomatic as before and for the reasons I mentioned in my last answer which is that knowledge of this variant is not fundamental to our management of the pandemic there is no reason why people need to know or will know necessarily because of the small number of labs that do this variant whether they have it or not is not material they do need to isolate if they have symptoms they need to self isolate if they are a contact and they need to ensure the social distancing as before. So Tom I don't feel that there are political issues at stake here as you heard Chief Medical Officers were meeting last week including on Friday night as the latest information emerged we had a rapid four nation meeting on Saturday morning that allowed me to assemble the Welsh cabinet here during Saturday afternoon there are further conversations planned for later today all of that will allow us to make sure that the points that you are raising on behalf of the most clinically vulnerable are discussed and shared between us. For my second question this is about shielding how will the advice for those on the shielded patient list be changing given the emergence of a new variant of COVID-19 and linked to that will the new strain trigger increased benefits for example you as in Northern Ireland tell us that those who get the personal independent payment will receive an extra 200 pounds to make higher heating costs. That final point Tom is only possible because Northern Ireland has its own separate social security system whereas England, Wales and Scotland share a single system which is controlled by the UK Government through the DWP so if there's an opportunity we'll find out if they are making any plans there. On the advice of the shielded group I know that the deputy chief medical officer has been involved in discussions about this this morning so I'll let him report on that. Yes I mean we're all concerned for those people who are clinically extremely vulnerable and they will know who they are and be concerned as well. Although the virus is more transmissible the illness we think is the same but still the risk is there isn't it and we will reflect on what we understand over the course of the Christmas week and we'll write to everybody on the shielding list straight after Christmas. In the meantime we will look at our advice on the Welsh Government website as well to see if that needs to be updated and in some cases strengthened as well. Tom thank you to Alan Evans at Llanelli online. First Minister it's a very bleak picture but I will assure your team on your family, Nadolig Chlawing, a bloethau newidau. Is there a case for balancing and applying similar government interventions within the NHS and in people's lives given that the numbers of people who have died of prevalent cases causes other than COVID-19 is high and likely to rise if the might of the NHS is disproportionately driven towards COVID-19 or do you see COVID-19 as a must win at all cost problem and if so can we expect more doctors, more nurses, more people in the communities of Wales dealing with the effects of the pandemic or are you pinning all your hopes on a vaccine which will have to deal with this mutating virus? Well Alan diolch yn fawr am y dymyniadau gorau gyda'r un peth i chi wrth gwrs. Well I think your question goes straight to the heart of the dilemma that we've been trying to resolve in the Welsh Government. I've said a few times here I don't want to see the Welsh NHS become a national COVID service rather than a national health service so the reason we have taken the actions we have and the reason we ask everybody in Wales to pay particular regard over the coming weeks at those simple basic things we all have to do is in order that we get to the middle of next month whether NHS in Wales able to cope with people who are seriously ill with coronavirus but also having the capacity it needs to deal with everything else that we need it to do so it is absolutely a not an at all cost strategy that we are following in Wales it is a strategy designed to hang on to the gains that we made from May onwards when the health service was able to go back to resuming activity that had been paused in the first lockdown we don't want that to have to go into permanent reverse and the actions we have taken and the things we ask people to do will be absolutely crucial in making sure that the NHS is there for everybody. You did allude to it earlier on you just you did mention the military very briefly and we're at level four obviously I mean this thing keeps going are there further measures the UK and Welsh Government could and would take if the situation becomes any bleaker than it already is and would those measures involve the utilisation of the armed forces in any way? Well I'm very grateful indeed for all the help we've had from the armed forces during the whole of the coronavirus experience we had a huge amount of help in the very beginning both in planning and logistics but also in very practical things like ambulance driving and cleaning of ambulances so they could get back on the road again quite rightly as things improved over the summer the army began to withdraw from those activities and we were absolutely happy to cooperate in that happening in recent weeks we've had to draw back again on help from the armed forces and I was involved in signing off things to ask for some further help even over this weekend so we've we've had all the help we could have asked for and the message to us always is that if more help is needed we should ask and if if that help is available I'm sure we will get it so at the moment we've asked for everything we think we currently need but in the sense of the door is always open we remain extremely grateful for the help that we that we receive. Diolch yn fawr, ffynu ffordd disart yn un i gareth at the Caerphilly Observer. Diolch, pryn o'n dda, both. Professor Jones first, for people who may be thinking what does this new strain mean for me and how I limit my personal risk? Do we yet know exactly sort of in layman's terms what makes this new variant 70% more transmissible for example is it more resistant to hand washing and hygiene or does it last longer in suspension in the air in indoor spaces for example and how does that impact what people should be doing in their daily routines? Well we don't know for certain we have no evidence that the thing lasts for longer in the atmosphere or on surfaces or is resistant to hand washing and what I think we do know is that the two of the changes in this virus are in the spike protein area and it is this area which binds to a receptor within human cells and seems to account for a greater binding affinity or greater stickiness for human cells so when it comes into contact with cells it may be more likely to be sticky and then we also believe that there are reasons why maybe then the genetic material within the virus can more easily enter the cell and as a result of that I think there is also emerging evidence that people who have this variant have a higher viral load and therefore may give off a little bit more virus too so it's more sticky it probably has more puncture ability in terms of human cells and perhaps people are giving off the virus more. Diolch yn fawr. Another question now a final question then to the first minister on schools teachers here in Caerphiliana Crosswell continue to ask when they'll receive data on transmission in schools regarding their safety when they go into work. Can teachers across Wales expect to see data regarding the impact that this new strain will have on their safety in their workplace before they're asked to return in January? Are there any discussions in place to upscale the priority for vaccinating teachers in the not too distant future? Well Gareth I think we publish data very regularly we share it with the trade unions and so on about the situation in schools the number of young people and staff members who contract the virus. You will know that we did whole town testing in Murther and they're now doing some in the Cynon valley in that tested every pupil in secondary schools in Murther. The positivity rate was less than 1%. There were 440 odd pupils tested in mountain ash comprehensive school and one of them turned out to be positive. So I think on the whole the evidence is is that teachers are not significantly more exposed to the virus because of the job that they do than would be true of people in the general population but we have plans for after the Christmas period for serial testing of people who are tested of people in schools who come into contact with somebody who has tested positive in order to give those people confidence that they themselves are not positive and to allow people to stay in the school setting for longer. I think all the way through our approach has been to share information because I think often the information turns out to have some reassuring aspect to it as well as pointing out where concerns need to be responded to and we'll continue certainly to do that in relation to teachers, other members of staff in schools and to school students. Diolch yn fawr. Thank you all very much indeed.


Welcome back. As I said earlier, we will be now looking at continuous probability density functions. The random variable x may either be discrete or continuous. It may take individual discrete values or it may take values within a continuous range, okay. What I mean by a continuous range is even decimal numbers can be included. For example, mole fraction lies between 0 and 1 but it can take any value between 0 and 1.53, 0.54 and so on. Whereas if you roll a die, you can have only discrete entities like 1, 2, 3, 4, 5 and 6. So it may take real numbers which may range between minus infinity to plus infinity. One of the important property of a random variable whether it is continuous or discrete is it has a probability distribution function associated with it. The probability distribution function simply means the probability associated with the random variable taking on a particular value or falling within a range of values. In the case of discrete probability distributions, the probability of a random variable taking a particular value may be given. In the case of continuous random variables, you do not talk of the probability of the random variable taking a particular value but you talk of the random variable taking a value between a certain range, okay. We will be discussing more on this shortly. Whenever there is a chemical reaction taking place in a reactor, the products of the reaction are measured by using several analytical means. For example, you may use a gas chromatograph or a HPLC or you may even use simple titration methods to find the concentration of the products. And so the values can be practically continuous. Usually the values beyond 3 digits after the decimal point are not reported. You give only up to 2 to 3 digits depending upon the accuracy of your instrument. Another example of the continuous random variables is the case or situation involving the heating of water kept outside in the sun. Let us take a bottle of water from the fridge. It may be around 10 or 15 degree centigrade and then we keep it out in the sun. The temperature of the water will increase and if you are measuring the temperature with a thermocouple, it can show values that are anywhere between let us say 15 degree centigrade to let us say 35 or 40 degree centigrade, okay. And these values are continuous. The thermocouple depending upon the accuracy may be reporting up to 2 decimal places. So the point here is we are not having discrete temperature values but the temperature values varying over the range between 15 degree centigrade to say 35 or 40 degree centigrade. We cannot talk of the probability of a random variable taking a particular value x in the case of continuous probability distributions, okay. Here the probability of the random variable taking a specific value within the range is actually 0. I am going to give the reason for it. Let us consider a conical block of wood which is having different colored sections. You can see that it is terminating in a point and then expanding to the base. Now if you want to find the weight of the wood at the point, okay, obviously the weight of the wood at the point is 0 but if you take a certain section of the wood, let us say covered by the green portion, it will have a certain weight. If you add up all the colored portions, you are going to get the total weight of the wood. So we want to find the mass of the wood starting from the pointed edge x is equal to 0 and eventually moving towards the flat base x is equal to L. Since the mass is equal to volume times density, when the length is equal to 0, the volume is also equal to 0 and hence the mass will be 0. The green portion however occupies a certain length and it occupies a certain volume and so it will have a certain mass. Let us take any distance from the pointed edge, okay. Let the distance be horizontal and let it be denoted by A. The mass of the conical block of wood until the point A is given by equals rho into integral of 0 to A pi r squared dx, okay. The need for integration arises because r is changing with x. The radius of the conical block of wood is varying with distance. So you would like to do the integration and find the mass. A can be anywhere between the conical tip to the base. In order to carry out this integration, you need to find out the relation between the radius and x, the distance from the tip, okay and that can be easily found. The important thing to note here is the weights are continuously distributed over a length x and the weight of the object up to a point A may be found by integrating the weight distribution function up to that point. The same concept we can use to describe the probability density function. It describes the distribution of probabilities in the continuous random variable domain, okay. So the probability that the random variable x will take a particular value within that range is actually 0 just as the weight of the wood at a particular point is 0. So in order to find the weight of the wood, we have to take a certain portion of the wood. In the same way, in continuous probability distributions, we want to find the probability of the random variable x falling between 2 values within the range, okay. You can even start from the lower limit of the continuous random variable range up to a certain point in the same range. You will have a non-zero probability. We may interpret a probability density function f of x as 1 that assigns probabilities in such a manner that probability of x less than or equal to a equals probability of x less than a is given by minus infinity to a f of x dx. So we are doing the integration here and if you look at the slide, it can be seen that we have probability of x less than or equal to a or probability of x less than a. It is immaterial whether we put x less than or equal to a or x less than a. Since the probability of the random variable taking a particular value, okay a specific value 0, it is immaterial whether we use the less than or equal to sign or less than sign. We have the probability density function or the probability distribution function f of x. We then integrate it between the lower limit to the required value a. In many practical situations, the random variable may not take a value of minus infinity. For example, if you are crushing the rock, the smallest particle size may be very, very small in the order of let us say 1 micrometer, okay. So definitely it is not minus infinity, it is not even negative. But in some cases we take the logarithm of such values and so it may become negative, right. The upper limit also need not be plus infinity, it may be a finite value. So if you are having a finite lower limit and a finite upper limit, the random variables value beyond these limits will be definitely 0, okay. It will take only values within the specified interval. It is assumed that beyond this interval, the random variable value is going to be 0. So again coming to the definition of the probability density function, probability of the random variable taking a value less than or equal to z. So we put that z in the upper limit of the integral sign and then we call it as the f of z, okay. This f of z is also a familiar quantity to us. It is nothing but the cumulative distribution function for the continuous random variable x, okay. It is as if you are accumulating or aggregating the probabilities up to z and so it is called as the cumulative distribution function. Earlier we were using the sigma sign for adding up the probabilities. Now we are using the integral sign. This is an example of a continuous probability density function. You can see that beyond minus 100 and plus 100, there are literally no points, okay. There are no representation of the data which means that your lower limit is minus 100 and the upper limit is plus 100. Even these values up to 100 on either side of the origin are pretty small but once you reach, let us say about 35 or so, the values start to increase and they reach a maximum value at the origin. This probability density function is symmetric in nature because the area under the curve on either side of the origin is the same. For example, if I take 0 to minus 10, I find the area under the curve. That will be same as the area under the curve from 0 to plus 10. This is an example of a symmetric distribution but not all distributions need to be symmetric. Some of the distributions may have skewness. They may be having an orientation towards the lower values or a preference for lower values and so they may be having a peak earlier and then they may have a long tail. Let us look at some of the features of probability density functions. The area under the curve is equal to 1. If you recall the discussion for discrete probability distributions, sigma f of xi was equal to 1 which means that if you add up all the random variables probabilities, then they should add up to 1. Similarly, when you take the area under the curve which represents the probability distribution, you should get 1. So, essentially we are saying what is the probability of the occurrence of the values of x between the upper and lower limit. We are including all the values between the upper and lower limit and the probability will be equal to 1. So, we are really more interested in finding out the probabilities of the random variable lying between 2 values or 2 numbers. Here we are more interested in a specific value a, a specific value b which do not correspond to the lower limit or upper limit, okay. We can sometimes relax the restriction. We can even put a as the lower limit or b as the upper limit but both of them may not be the limiting values. If your range is between let us say 0 to 10, okay, we may be interested in finding the probability of the random variable taking a value between 2 and 4 or any value, okay. So, in such a case the answer is not equal to 1, it will be a value lower than 1. For that we need to do the integration. We take the limit a to b for the integration and then integrate f of x between these 2 limits. This may be written as – infinity to b f of x dx – – infinity to a f of x dx. That will give us the area under the curve between a and b and that is nothing but the difference between the 2 cumulative distribution functions. The cumulative distribution function evaluated at b and the cumulative distribution function evaluated at a. So, we get f of b – f of a. Suppose the 2 numbers a and b are such that they are very close to each other. Let us say that one values z and the other values z plus delta z. We want to find the probability between z and z plus delta z. So, what we do is we integrate between z and z plus delta z f of x dx. If delta z is very small, okay, then we can write probability of z less than or equal to x less than or equal to z plus delta z as f of z times delta z. In the small range of z to z plus delta z, f of x takes the value f of z and it does not change significantly in this small interval. So, we may as well write it as f of z and since it is constant between these 2 values or pretty much constant between these 2 values, we may take it outside the integral sign and then simply evaluate dx between z and z plus delta z and we get f of z delta z. Please remember this result. We will be using it shortly. Now, we want to find the relation between the probability density function and the cumulative probability distribution function. In other words, we have to find the relation between small f of x and capital f of x. So, the definition for the cumulative distribution function corresponding to z plus delta z that is probability of x less than or equal to z plus delta z is equal to minus infinity to z plus delta z f of x dx.  So, we can write it as f of z plus delta z equals minus infinity to z plus delta z f of x dx. We also know on the same lines that f of z equals minus infinity to z f of x dx. Hence the probability of the random variable x lying between z and z plus delta z may be written as f of z plus delta z minus f of z. The last 2 f's are capital F's representing the cumulative probability distribution. However, just a brief while ago we saw that probability of z less than or equal to x less than or equal to z plus delta z was more or less equal to f of z delta z. So, we may write f of z delta z as the difference between the 2 cumulative probability distributions.  We can now write after dividing by delta z f of z is equal to limit of delta z tending to 0 f of z plus delta z minus f of z by delta z and that is equal to f of z is equal to df of z by dz. We are now taking the derivative of the cumulative distribution function with respect to z. Then we retrieve or get the continuous probability density function. It is quite simple in fact, you please recall that when we wanted to get the cumulative distribution function we carried out the integration. Now, when you want to get the probability density function from the cumulative distribution function we have to carry out the differentiation. We differentiate the cumulative distribution function f of z with respect to z to get the small f of z. Changing the variable from z to x we get f of x is equal to d capital f of x by dx. So, when you are given the cumulative distribution function you can obtain the probability distribution function or the probability density function by simple differentiation. When the cumulative distribution function is given in the form of equation, you can differentiate this equation with respect to the independent variable and retrieve the continuous probability density function. You can retrieve the continuous probability density function. Sometimes you are going to get only experimental data. You may not have a mathematical model to that equation. Then you may have to carry out numerical differentiation to get the form or shape of the probability density function. These are simple elementary calculus. A certain query may arise when you are handling the probability density function. We know the area under the curve is equal to 1. Integral of f of x dx is equal to 1 but can the f of x value itself be greater than unity. So, that is a very interesting question. If the area under the curve of the function x is equal to 1, can the value of f of x exceed unity? There is no restriction on the value of f of x provided it is real. It should be also positive value. And beyond this there is no real restriction on the range. You should also note that the constraint integral of a to b f of x dx is equal to 1 should be satisfied. So, if f of x value takes greater than 1 numbers, then the upper and lower limits should adjust accordingly so that this constraint is satisfied. Let us take a simple case where the function is given by Mx. So, when you integrate Mx between the limits a to b, you get Mx squared by 2 or M by 2 into b squared minus a squared and since that will be equal to 1, M by 2 into b squared minus a squared is equal to 1, M will be equal to 2 by b squared minus a squared. Then the value of M increases okay, the b will decrease and approach a so that the constraint of the area under the curve being equal to unity is satisfied. To demonstrate this with respect to this figure, if the value of f of x keeps increasing or goes to a higher value, then the width will start to shrink and the lower limit and the upper limit will start approaching each other. So, when the curve tries to grow upwards, it sort of becomes thinner and thinner okay, the limits approach each other. In the discrete probability distribution analysis, we came across the mean mu and the variance sigma squared. How are these parameters defined for the case of the continuous random variable? In fact, the definitions are quite similar. We use integration sign here while we use the summation sign for the discrete case. Let us look at the mean of the probability density function. Mu is equal to the expected value of the random variable x okay. So, we have mu is equal to minus infinity to plus infinity x f of x dx. This is the definition for the mean or the average value for the continuous distribution. We can also define the variance of the probability density function. The variance is defined as the expected value of x minus mu whole squared. Here x is the random variable. For continuous distributions, we have sigma squared is equal to minus infinity to plus infinity x minus mu whole squared f of x dx. We can expand the x minus mu whole squared and try to simplify this integral.  What happened here is we multiply f of x with x squared and take it out. We have a separate integral minus infinity to plus infinity x squared f of x dx minus 2 mu x f of x dx became minus 2 mu squared using the definition for the mean and then you have mu squared f of x dx. When you integrate that minus infinity to plus infinity f of x dx is equal to 1. So, you get minus 2 mu squared plus mu squared which reduces to minus mu squared. So, sigma squared the variance of the probability density function is equal to minus infinity to plus infinity x squared f of x dx minus mu squared. The variance is an estimate of the spread of the distribution. To find the standard deviation, you take the square root of the variance and report the positive value. By now, you may have also noticed that sigma squared plus mu squared is expected value of x squared. This result we have also seen in the case of discrete probability distributions. E of x squared by definition is minus infinity to plus infinity x squared f of x dx. These are parameters which we will be frequently coming across in continuous probability distributions. Some of you may be having the apprehension perhaps that every time you may have to do the integration to find the mean and variance. Usually, we will be working with standard probability distributions for which the mean and variance are well known. So, we do not really have to do the integration every time. The next query is suppose I want to find the probability of the random variable x lying between 2 numbers, okay. Should I do the integration? For standard probability distributions, tables of data are available for finding out these probabilities. In case the function is unknown or a new function which has not been studied previously, then of course, you will have to carry out the integration. If the integration is not possible analytically, you may have to carry out the integration numerically. Nowadays, the softwares are so advanced that either carrying out the numerical integration or even the analytical integration is not a big task. If you look at standard software spreadsheets, numerical computation programs, MATLAB, they all can directly give you the value of the probability when you specify the limits of the probability distribution function. The probability values are automatically calculated and given. I would encourage you to look at some of these spreadsheets and mathematical software to find out the probabilities for some standard distributions. I would like to encourage you to look at these spreadsheets or mathematical software. You can find out using the help command how to find the probabilities for standard distributions. They are very easily calculated through simple commands. The standard probability distributions which we will be studying are the normal distribution of the Gaussian distribution, the student's t distribution, the Fisher distribution and the chi-squared distribution. There are also other distributions like the beta distribution, the gamma distribution, the Weibull distributions and so on. But once you have had the background for these standard distributions which I am going to talk about, you can very easily understand the other ones. So right now we will conclude our discussion on the continuous probability distributions and go on to the most important distribution, the normal distribution.