The picture above is a screenshot from a brilliant online epidemic calculator. It’s based on a standard infectious disease model, SEIR (Susceptible-Exposed-Infected-Removed), for which references are included in the same link. The calculator lets you choose various settings for an epidemic, and shows you how the epidemic is expected to progress, both before an intervention – shown by the vertical black dashed line – and after. The default settings for the calculator seem to be set at current best estimates for the current Coronavirus outbreak. The screenshot above is based on these default settings, but assumes a population close to 60 million. The different shaded regions in the graph correspond to counts of different aspects – fatalities, hospitalisations and so on – which you can choose to display or hide.
One of the main settings in the model is something called the ‘basic reproduction number’, written . This is the average number of people an infected person will infect, and is given by
where E is the number of contacts made and p is the probability of transmission.
I discussed in an earlier post how the value of determines the trajectory of the epidemic: if it is greater than 1 the epidemic grows exponentially; if it’s less than 1 the epidemic fades out. For the COVID-19 outbreak a reasonable estimate for is thought to be 2.2, which is the default setting in the calculator.
So, one thing you can do is change the value of and see how it changes the epidemic evolution. Other settings in the model are likely to be less well estimated, but by experimenting with values in the calculator it’s interesting and useful to see which aspects cause the trajectory to change dramatically and which have very little impact.
The other interesting feature of the calculator is that it allows you to see the effect of an intervention such as social-distancing. You simply choose by what percentage is reduced. For example, in the screenshot above, it’s assumed that is reduced by 2/3 to 0.73. The light-blue shaded region shows how – under the given settings – the number of hospitalised individuals continues to grow for a further month or so, before tailing off. Obviously, whether social distancing results in a 2/3 reduction in is anybody’s guess, but again you can experiment with this value to see how different degrees of conformity to the guidelines are likely to impact on the epidemic trajectory.
Was the UK government too slow in introducing a full-scale lockdown? You can slide the vertical black line left or right to see what the effect of introducing social control measures just a few days earlier or later would have been.