A geometric analysis of the SIRS epidemiological model on a homogeneous network

TL;DR

This paper analyzes a fast-slow SIRS epidemiological model on homogeneous networks using geometric methods, revealing the emergence of periodic solutions unlike traditional homogeneous mixing models.

Contribution

It introduces a geometric analysis of a fast-slow SIRS model on networks, deriving reduced maps and demonstrating the existence of periodic solutions.

Findings

Model exhibits periodic solutions not seen in homogeneous mixing models

Fast-slow dynamics are captured through 2D and 1D maps

Bifurcation analysis reveals complex dynamical behavior

Abstract

We study a fast-slow version of an SIRS epidemiological model on homogeneous graphs, obtained through the application of the moment closure method. We use GSPT to study the model, taking into account that the infection period is much shorter than the average duration of immunity. We show that the dynamics occurs through a sequence of fast and slow flows, that can be described through 2-dimensional maps that, under some assumptions, can be approximated as 1-dimensional maps. Using this method, together with numerical bifurcation tools, we show that the model can give rise to periodic solutions, differently from the corresponding model based on homogeneous mixing.