Mathematical modelling and empirical data analysis of the Covid-19 pandemic
Hoang Duc Luu and Jürgen Jost
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Submission date: 20. Jul. 2020 (revised version: July 2020)
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The SIR model is the basic mathematical model for epidemics, but it needs some modification to capture the dynamics of the current Covid-19 pandemic. Here, we consider contact rates that depend on the total number Γ of infections. Under general assumptions, the recovery and death rates then become increasing functions of Γ. To make the model realistic, we also need to introduce time delays corresponding to the incubation and the duration of the disease, and we shall treat them as random variables. Population structure is another issue, for instance concerning the contact number distribution. We develop and describe such models and show how the coefficients can be estimated and what the effects of delays are. We find that a simple linear regression is adequate for modelling the decay of the epidemic.