Basic estimation-prediction techniques for Covid-19, and a prediction for Stockholm

Tom Britton

Suppose that a set of preventive measures are put in place at some calendar time t p still assumed to be in the early phase of the epidemic. Here we assume that this effects the rate of infectious contacts but not the (mean) generation time g = 1/γ. Most preventive measures agree with this: school closure, self-isolation, closing (or reduced activities) of restaurants, bars, cinemas. There are also some preventions which aim at reducing g, such as contact tracing followed by isolation, but here we restrict ourselves to preventions reducing λ. We assume that the new preventive measures have the overall effect of reducing λ by a factor ρ, so that the new effective rate of contact equals λ E = λ(1 − ρ), and the new effective reproduction number equals R E = (1 − ρ)R 0 . For covid-19 there is currently no available vaccine, but for situations where there is it is also possible to include vaccination of a fraction of the community as a preventive measure. In this case, the factor ρ also includes effects from vaccination. If for example a fraction v are vaccinated with a vaccine giving perfect immunity then this results in ρ = v if this is the only preventive measure.