Stationary states and spatial patterning in an $SIS$ epidemiology model with implicit mobility

TL;DR

This paper investigates stationary states and spatial patterns in an SIS epidemiological model using cellular automata, analyzing how individual mobility and neighborhood size influence infection spread and pattern formation.

Contribution

It introduces a novel analysis of spatial patterning in an SIS model with implicit mobility, linking local behavior to a zero-dimensional logistic growth approximation.

Findings

Explicit dependence of infected fraction on curing rate derived

Spatial patterns of infection identified in stationary states

Model links local dynamics to global spatial patterns

Abstract

By means of the asynchronous cellular automata algorithm we study stationary states and spatial patterning in an $SIS$ model, in which the individuals' are attached to the vertices of a graph and their mobility is mimicked by varying the neighbourhood size $q$. The versions with fixed $q$ and those taken at random at each step and for each individual are studied. Numerical data on the local behaviour of the model are mapped onto the solution of its zero dimensional version, corresponding to the limit $q\to +\infty$ and equivalent to the logistic growth model. This allows for deducing an explicit form of the dependence of the fraction of infected individuals on the curing rate $\gamma$. A detailed analysis of the appearance of spatial patterns of infected individuals in the stationary state is performed.