Persistence, extinction and spatio-temporal synchronization of SIRS cellular automata models

TL;DR

This paper investigates how mobility and multi-patch environments influence the persistence and extinction of epidemics in SIRS cellular automata models, revealing phase transitions, oscillation behaviors, and the impact of spatial factors.

Contribution

It extends traditional models by incorporating individual mobility and multi-patch dynamics, analyzing their effects on epidemic persistence and extinction.

Findings

Higher mobility promotes epidemic persistence and causes phase transitions.

Lower coupling strength leads to anti-phase oscillations of infected populations.

Extinction time scales linearly with system size.

Abstract

Spatially explicit models have been widely used in today's mathematical ecology and epidemiology to study persistence and extinction of populations as well as their spatial patterns. Here we extend the earlier work--static dispersal between neighbouring individuals to mobility of individuals as well as multi-patches environment. As is commonly found, the basic reproductive ratio is maximized for the evolutionary stable strategy (ESS) on diseases' persistence in mean-field theory. This has important implications, as it implies that for a wide range of parameters that infection rate will tend maximum. This is opposite with present results obtained in spatial explicit models that infection rate is limited by upper bound. We observe the emergence of trade-offs of extinction and persistence on the parameters of the infection period and infection rate and show the extinction time having a linear relationship with respect to system size. We further find that the higher mobility can pronouncedly promote the persistence of spread of epidemics, i.e., the phase transition occurs from extinction domain to persistence domain, and the spirals' wavelength increases as the mobility increasing and ultimately, it will saturate at a certain value. Furthermore, for multi-patches case, we find that the lower coupling strength leads to anti-phase oscillation of infected fraction, while higher coupling strength corresponds to in-phase oscillation.