Modelling the Spread of an Epidemic in Presence of Vaccination using Cellular Automata

TL;DR

This paper develops a cellular automata model to simulate epidemic spread with vaccination effects, capturing spatial dynamics and growth rates more effectively than traditional models.

Contribution

It introduces a CA-based approach to model epidemic spread and vaccination, providing spatial and growth insights beyond mean-field models.

Findings

CA model aligns well with SIR results

Vaccination effects incorporated successfully

Spatial spread characterized by linear front motion

Abstract

The results of Kermack-McKendrick SIR model are planned to be reproduced by cellular automata (CA) lattice model. The CA algorithms are proposed to study the model of epidemic, systematically. The basic goal is to capture the effects of spreading of infection over a scale of length. This CA model can provide the rate of growth of the infection over the space which was lacking in the mean-field like SIR model. The motion of the circular front of an infected cluster shows a linear behaviour in time. The correlation of a particular site to be infected, with respect to the central site is also studied. The outcomes of CA model are in good agreement with that obtained from SIR model. The results of vaccination have been also incorporated in the CA algorithm with a satisfactory degree of success. The advantage of the present model is that it can shed considerable amount of light to the physical properties of the spread of a typical epidemic in a simple, yet robust way.