SI epidemic model applied to COVID-19 data in mainland China.

J Demongeot,Q Griette,P Magal

doi:10.1098/rsos.201878

J Demongeot, Q Griette + Show 1 more

Open Access

https://doi.org/10.1098/rsos.201878

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Abstract

The article is devoted to the parameters identification in the SI model. We consider several methods, starting with an exponential fit to the early cumulative data of SARS-CoV2 in mainland China. The present methodology provides a way to compute the parameters at the early stage of the epidemic. Next, we establish an identifiability result. Then we use the Bernoulli–Verhulst model as a phenomenological model to fit the data and derive some results on the parameters identification. The last part of the paper is devoted to some numerical algorithms to fit a daily piecewise constant rate of transmission.

Highlights

Estimating the average transmission rate is one of the most crucial challenges in the epidemiology of communicable diseases
We use algorithm 1 and we plot the rate of transmission obtained by using the reported cases of COVID-19 in China where the parameters are fixed as f = 0.5 and ν = 0.2
It is often shown that many sets of parameter values are compatible with a good fit of the observed data

Summary

Introduction

Estimating the average transmission rate is one of the most crucial challenges in the epidemiology of communicable diseases. This rate conditions the entry into the epidemic phase of the disease and its return to the extinction phase, if it has diminished sufficiently It is the combination of three factors, one, the coefficient of virulence, linked to the infectious agent (in the case of infectious transmissible diseases), the other, the coefficient of susceptibility, linked to the host (all summarized into the probability of transmission), and the number of contacts per unit of time between individuals [1]. — S0 > 0 the number of susceptible individuals at time t0 when we start to use the model; — 1/ν > 0 the average duration of infectious period; — f > 0 the fraction of reported individuals; are known parameters. The actual number of susceptibles S0 can be smaller since some individuals can be partially (or totally) immunized by previous infections or other factors This is true for SARS-CoV2, even if COVID-19 is a newly emerging disease. The recent survey by Byrne et al [9] focuses on this subject

Result

29 Feb 2020

19 Feb 26 Feb 04 Mar 11 Mar 18 Mar 25 Mar 01 Apr 08 Apr 2020

Computing numerically a day-by-day piecewise constant rate of transmission

Numerical simulations

Discussion