Basic prediction methodology for covid-19: estimation and sensitivity considerations

Tom Britton

We end the methodology section be given predictions of the total fraction getting infected, and perhaps even more important, the expected number of case fatalities. We assume that the same set of preventive measures (if any) remain constant through main part of the epidemic. The results are not valid if the they were put in place after a few percent had been infected, nor if they were varied during the main part of the outbreak (the prediction problem is then much more complicated and better suited for simulation studies). Suppose hence that reproduction number equals R (equal to R 0 if no preventive measures are put in place, or otherwise R E ). The final fraction τ getting infected is known to solve the equation 1 − τ = e −R 0 τ [4] , a solution which has to be obtained numerically. In case the community is heterogeneous in one or several ways, the final fraction getting infected is usually 5-20% smaller than this solution. So, given that the reproduction number is known the final fraction getting infected is well-predicted. The estimate is of course sensitive to R, but if R ≥ 2 then τ ≥ 75%, so it is not too sensitive to exakt values of R in case it is above 2 or so.