SIRS dynamics on random networks: simulations and analytical models

TL;DR

This paper investigates the limitations of the pair approximation model in predicting sustained oscillations in the SIRS epidemic model on random networks, comparing analytical predictions with simulation results.

Contribution

It analyzes how the oscillatory phase in the SIRS model depends on network degree and highlights discrepancies between pair approximation predictions and simulation outcomes.

Findings

Simulations often die out or show damped oscillations instead of sustained ones.

Standard pair approximation fails to capture the qualitative behaviour of large network simulations.

The oscillatory phase's dependence on network degree is characterized.

Abstract

The standard pair approximation equations (PA) for the Susceptible-Infective-Recovered-Susceptible (SIRS) model of infection spread on a network of homogeneous degree $k$ predict a thin phase of sustained oscillations for parameter values that correspond to diseases that confer long lasting immunity. Here we present a study of the dependence of this oscillatory phase on the parameter $k$ and of its relevance to understand the behaviour of simulations on networks. For $k=4$, we compare the phase diagram of the PA model with the results of simulations on regular random graphs (RRG) of the same degree. We show that for parameter values in the oscillatory phase, and even for large system sizes, the simulations either die out or exhibit damped oscillations, depending on the initial conditions. This failure of the standard PA model to capture the qualitative behaviour of the simulations on large RRGs is currently being investigated.