Working Paper Article Version 1 This version is not peer-reviewed

# An Epidemic Grid Model to Address the Spread of Covid-19: A Comparison between Spain, Italy and UK

Version 1 : Received: 5 January 2021 / Approved: 6 January 2021 / Online: 6 January 2021 (14:49:09 CET)

A peer-reviewed article of this Preprint also exists.

Signes-Pont, M.T.; Cortés-Plana, J.J.; Mora-Mora, H. An Epidemic Grid Model to Address the Spread of Covid-19: A Comparison Between Italy, Germany and France. Math. Comput. Appl. 2021, 26, 14. Signes-Pont, M.T.; Cortés-Plana, J.J.; Mora-Mora, H. An Epidemic Grid Model to Address the Spread of Covid-19: A Comparison Between Italy, Germany and France. Math. Comput. Appl. 2021, 26, 14.

## Abstract

This paper presents a discrete compartmental Susceptible-Exposed-Infected-Recovered/Dead (SEIR/D) model to address the expansion of Covid-19 pandemic. When time passes, the status of the cells is determined by binary rules that update following both a neighbourhood and a delay pattern. The model assumes the environmental parameters have a crucial impact on the expansion of the disease so a grid is assigned to each parameter to model the single effect caused by this parameter. The expansion is then the weighted sum of all the grids. This proposal shows how the grid architecture, along with an update rule and a neighbourhood pattern is a valuable tool to model the pandemic expansion. This model has already been analyzed in previous works and compared with the corresponding continuous models solved by ordinary differential equations (ODE), coming to find 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 illness. The delays (between Susceptible and Asymptomatic, Asymptomatic and Infected, Infected and Recovered/Dead) may have a crucial impact on both 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.

## Keywords

Covid-19; computational modelling; space time framework; multigrid implementation; update binary rules; Von Neumann and Moore neighbourhoods.

## Subject

Computer Science and Mathematics, Algebra and Number Theory