Modelling the coronavirus outbreak

The new coronavirus responsible for the outbreak of Covid-19 disease remains steadfastly at the top of the news agenda. And in the last week or so, the focus has moved from the far East to Europe, which is now regarded as the epicentre of the outbreak. But, unlike some of our European neighbours - and other nations internationally, which have locked down their countries, restricted people movements, closed schools and businesses, and banned large social gatherings, the UK has delayed instituting many of these measures. But is this the right approach? The strategy being followed is based on mathematical models of how diseases spread, together with assumptions about how long people can reasonably be expected to comply with various interventions. Impacts on the economy and health service are also taken into account. Jordan Skitrall is an infectious diseases doctor and a mathematician specialising in modelling disease spread at Cambridge University. Chris Smith asked him how maths is being used to understand and plan for the spread of the new coronavirus...

Jordan - One way we often think about this is a mathematical concept called R0. The basic reproduction number, and R0 is the answer to the question: On average, if we had a person infected with this disease in a population, all of whom are susceptible to it and can get it, how many people would it go on infect? And at the beginning of the disease outbreak, when we're able to work out how many new infections there appear to be for each single person who's getting the infection, because we're able to follow them all up, we can just count the number of people getting infections. As long as we're able to trace the people who might've got the infection from the first person with the disease.

Chris - The UK government, when they did various press announcements around this said; we anticipate, on a worst case basis, 80% of the population will get this. Where did they get that number from? How did they arrive at that?

Jordan - This is not so much a question of how fast is it going to spread throughout the population, as when it's finished spreading, how many people have it. And of course if you have something that spreads very well through a population, eventually everyone's going to have it. So what the question comes down to, is more of an issue of how many people will there be left when the disease is no longer capable of spreading. And there are two factors in that. One is you have some people in a population who are less susceptible, perhaps because they're less connected to other people in the population. But the other thing is that as more and more people get the disease in the population, they become immune to that disease afterwards, and at that point they can no longer pass it on. This is another way reducing the effective reproduction number, and that's the idea behind immunisation as well.

Chris - Essentially then, the infection creates its own herd immunity effect, where eventually the distance as it were, between susceptible individuals becomes so great that the virus just can't sustain a transmission chain anymore, in order to get to that final 20% at least in its first movement through a population.

Jordan - Precisely. And you've alluded in that last comment, to what we see historically with other viruses such as measles, where what happens is it spreads very efficiently. So the basic reproduction number of measles is somewhere around 10, and if you have a completely susceptible population, it goes through the entire population very quickly. But then because pretty much everybody has had it, it can no longer sustain. And so what happens is a little while down the line, typically a few years, where more people have been born, you get another outbreak of that same disease.

Chris - So when the chief medical officer says; we're going to institute various mechanisms, which might include things like closing schools, closing universities, stopping people moving on public transport, that will be informed by some point on the model where people will have said; at this point, if we intervene, it will actually have a meaningful effect, which is what's informing why they haven't yet just followed suit with other countries in Europe, say?

Jordan - Exactly. Doing this kind of intervention will have an effect later on. You could say, well why aren't we doing it now? Because it will have an effect earlier on. But if we reduce the rate of increase from a small number of cases, we still get that small number of cases.

Chris - When you were saying the rate of change, we're talking about really how steeply the graph is of cases, how fast it's climbing? And if you intervene too early, you're just changing a small number to another small number. Whereas if you go in at the right time, when it's getting really steep and about to climb really rapidly, and you bend the curve there, actually the change you're going to make is going to be more dramatic.

Jordan - Exactly. And so you have to ask the question, when is the best time to do this? Bearing in mind that it's already spreading throughout the population. In an ideal world, you might say; well, we should all go home and shut ourselves in our individual rooms for a number of weeks. Yes, that would slow things down the most, but that's not entirely realistic.

Chris - Is that not just kicking the virological can down the road. Because I'm a susceptible individual now. If I go and shut myself in my bedroom for two weeks, I'm going to come back two weeks from now, still a susceptible individual and I'll just catch it then won't I?

Jordan - The answer is yes, but, one is in relation to that question you asked earlier about the total number of people who eventually get infected, and whether it might be possible to change that, because you might take some of these people who are less connected, who would have got the disease and just push them over this threshold to not getting it. And the other question is one of when people are going to get the disease. This relates to how are we going to treat people for this disease. Some people are going to require supportive treatments in hospital, things like being put on oxygen, and possibly more invasive treatment than that. And bearing in mind that we have assessed the number of intensive care beds. What we want to try to make sure is that we have the highest number of beds available for the most people. If we have the option between two people having the disease at the same time, and needing the same bed or two people having the disease at different times, and being able to occupy the bed in sequence, one would imagine that the outcomes are going to be better if we have these two people occupying the bed in sequence rather than trying to lie on top of each other.