A reaction-diffusion system to better comprehend the unlockdown: Application of SEIR-type model with diffusion to the spatial spread of COVID-19 in France

Youcef Mammeri

doi:10.1515/cmb-2020-0104

Abstract

Abstract We wondered that if a reaction-diffusion model considering only the mean daily movement of susceptible, exposed and asymptomatic individuals was enough to describe the spread of the COVID-19 virus. The model was calibrated using data on the confirmed infection and death from France as well as their initial spatial distribution. First, the system of partial differential equations is studied, then the basic reproduction number, 𝒭0 is derived. Second, numerical simulations, based on a combination of level-set and finite differences, shown the spatial spread of COVID-19 from March 16 to June 16. Finally, scenarios of unlockdown are compared according to variation of distancing, or partially spatial lockdown.

Highlights

A disease outbreak, called Coronavirus Disease 2019 or COVID-19 in brief, emerged in the city of Wuhan late 2019 [19]
We wondered that if a reaction-di usion model considering only the mean daily movement of susceptible, exposed and asymptomatic individuals was enough to describe the spread of the COVID-19 virus
The model gives an estimate of the expected number of cases in mainland China at the end of January 2020, as well as the global distribution of infected travelers. [22] fused

Summary

Introduction

A disease outbreak, called Coronavirus Disease 2019 or COVID-19 in brief, emerged in the city of Wuhan late 2019 [19]. The model gives an estimate of the expected number of cases in mainland China at the end of January 2020, as well as the global distribution of infected travelers. [5] incorporated daily movements in an SEIR model, while [8] proposed a statistical model to handle the di usion of covid-19 in Italy. Spatial propagation is translated by a di usion and the reaction terms are deduced from an extension from the classical SEIR model by adding a compartment of asymptomatic infected [1]. We aim at predicting the spread of COVID-19 by giving maps the basic reproductive numbers R and its e ective reproductive number Re. Do a reaction-di usion model, which consider only the mean daily movement of susceptible, exposed and asymptomatic individuals, describe correctly the spread of the COVID-19 virus?

Materials and methods

Results

March 16

Discussion