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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
80/2020

Mathematical modelling and empirical data analysis of the Covid-19 pandemic

Hoang Duc Luu and Jürgen Jost

Abstract

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.

Received:
Jul 20, 2020
Published:
Jul 20, 2020

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Preprint
2020 Repository Open Access
Hoang Duc Luu and Jürgen Jost

Mathematical modelling and empirical data analysis of the Covid-19 pandemic