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Modelling, past, present & future - Mr Ian Wright - 24 April 2020

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Good afternoon everyone, thank you for coming, and thank you Minister for inviting me to this briefing today to explain a little bit about the mathematical modelling that’s been done in an attempt to determine how the coronavirus epidemic might pan out on the Island, how it was used to help guide the DHSC’s preparations, and how it relates to what we’ve actually seen in the 5 weeks since the first positive case was identified here.

The first thing to say is that a model is simply a tool to help preparations – it’s not designed to make exact predictions as to exactly how many patients might be admitted on any particular day, or exactly when the peak of infections will arrive.

The basics of the model is that it is a mathematical function that gives a figure for how many new cases of covid may appear on a given day. It’s based on exponential growth, which is when the cumulative number of cases one day is a fixed multiple of the number of cases the previous day. We’re probably all familiar with the R value, which in epidemiology is the basic reproduction number. It is a figure that indicates how many people each infected person will give the virus to. The exact number is unknown, and depends on not just the virus itself, but on how people behave; A reasonable estimate for illustrative purposes for coronavirus would be R=3. Another important number is the time a person is infectious for, which for covid is about 5 days on average. So, if we have 1 case of covid, in 5 days time there will be another 3. Those three will infect 3 each over the next 5 days and so on. In that way we have a sequence of 1,3,9,27,81,243,729… new cases appearing every 5 days. It doesn’t take long until the infection is widespread.

A similar function was entered into an Excel spreadsheet, with a slight modification to take into account that cases can’t keep growing for ever as you eventually run out of people to infect, and this was used to generate the curves we’re all familiar with. The curves are presented as a set of 3, with a different daily growth rate. The blue curve, with the highest soonest peak, is a daily growth rate of 20%. In the first version of the model we used 29% as this was the figure calculated from the early phases of the epidemics in Italy and Spain, and I thought this probably represented the worst case scenario. It was changed to 20% because this is the growth we actually saw on the island before the effects of the lockdown 4 weeks ago came into being. So the blue curve represents what may have happened here if the government hadn’t brought in the restrictions in the latter half of March.

The middle red curve represents a growth rate of 12%. You can see that the effect of reducing the growth rate, which is what happens when you reduce R by introducing all the ‘stay-at-home’ measures, is to flatten the curve and push its peak to the right. In practice this buys you time to prepare the health service by freeing up capacity, re-purposing wards as intensive care units, training staff to run them, and reduces the level of peak demand so that your enhanced health service can cope, rather than ending up in a warzone situation, dreadful scenes of which we probably all saw from Northern Italy a month or so ago. The figure of 12% was what was seen in Germany, and what we thought would be achievable here, and so the red curve was used to guide planning at Nobles in terms of extra intensive care beds, dedicated Covid ward beds, PPE requirements, Oxygen need…

The orange curve represented what we thought was aspirational, or a best case scenario. It was generated with an 8% daily growth, which was a figure I calculated we might achieve if our lockdown measures were successful in halving the R value.

Since the lockdown measures took effect, on about the 3rd April looking at the log-plot of the actual case numbers here, our growth rate in cases has actually been lower than this so-called best case scenario. It’s averaged only 5.5%, and that includes the outbreak in Abbotswood which has accounted for the majority of the cases over the last 10 days or so. Without these, we’ve had only a few cases each day and none for the last 2 days, suggesting the spread in the wider community has all but stopped.

Health is perhaps the most obvious aspect of an epidemic to consider, but there are also major considerations with regard to society, psychological health and of course the economy. The sooner we can get back to a more normal way of life the better it will be for all of these aspects. It’s only sensible that plans to loosen the lockdown are gradual and monitored. Health is of course vital, and we must be confident that should any of the measures cause an increase in cases of covid that we’ll be able to cope with them. We’re currently well below the 12% growth used in the planning assumption, and calculations based on the small increase in R that may happen by letting the first sectors of the economy return to work indicate there should be a minimal effect on the current growth which will remain below this figure. In fact I’m fairly confident it will remain below the 8% ‘best case’ scenario. But this will of course be monitored very closely, specifically looking at what happens in 8-10 days time.

The modelling has, in many respects, done its job. We now need to focus more on monitoring the real situation here, not just with positive cases but also calls to 111, ED attendances and bed occupancy. Testing, and I’d like to pay tribute to Rizwan Khan and his team for such a sterling effort in getting the island testing to the stage we have it today, remains vital if we’re to keep the virus under control on island while slowly getting back to some semblance of normal living. In the meantime of course it remains vital that we keep up the social distancing, hygiene and self-isolation if required.