An Epidemic Grid Model to Address the Spread of Covid-19: A Comparison between Italy, Germany and France

Maria Teresa Signes-Pont,Higinio Mora-Mora,José Juan Cortés-Plana

doi:10.3390/mca26010014

Maria Teresa Signes-Pont, Higinio Mora-Mora + Show 1 more

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https://doi.org/10.3390/mca26010014

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Abstract

This paper presents a discrete compartmental Susceptible–Exposed–Infected–Recovered/Dead (SEIR/D) model to address the expansion of Covid-19. This model is based on a grid. As time passes, the status of the cells updates by means of binary rules following a neighborhood and a delay pattern. This model has already been analyzed in previous works and successfully compared with the corresponding continuous models solved by ordinary differential equations (ODE), with the intention of finding the homologous parameters between both approaches. Thus, it has been possible to prove that the combination neighborhood-update rule is responsible for the rate of expansion and recovering/death of the disease. The delays (between Susceptible and Asymptomatic, Asymptomatic and Infected, Infected and Recovered/Dead) may have a crucial impact on both height and timing of the peak of Infected and the Recovery/Death rate. This theoretical model has been successfully tested in the case of the dissemination of information through mobile social networks and in the case of plant pests.

Highlights

Since December 2019, the world has been facing the most serious pandemic since the Spanish flu pandemic of 1918
Many researchers have dedicated their efforts to coping with the dynamics of the spread of the disease; that is, they have provided insight into the underlying mechanisms of the virus propagation in order to guide the planning of the public health policies to ensure success in the fight against COVID-19
Reference [1] presents a summary of the Susceptible– Infected–Recovered (SIR) model and its variants SEIR and Susceptible–Unquarantined infected–Quarantined infected–Confirmed infected (SUQC) models, in order to highlight the relationship between the health measures to curb the pandemic and the mathematics behind them

Summary

Introduction

Since December 2019, the world has been facing the most serious pandemic since the Spanish flu pandemic of 1918. The outbreak has caused nearly 103,000,000 infections and more than 2,200,000 deaths as of the time of this publication. In response to this threat, all governments have ordered different degrees of containment measures, such as school and workplace closures, travel bans and quarantines, and have launched actions including social distancing, mandatory mask wearing, hand hygiene and viral or antibody testing campaigns as well as contact tracing using cell phone tracking. Many researchers have dedicated their efforts to coping with the dynamics of the spread of the disease; that is, they have provided insight into the underlying mechanisms of the virus propagation in order to guide the planning of the public health policies to ensure success in the fight against COVID-19. The time it takes for a cell to transition from one state to another fixes the delay between compartments

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