SIR model on a dynamical network and the endemic state of an infectious disease

TL;DR

This study investigates an SIR epidemic model on dynamic networks, revealing how network properties influence endemic disease states, with findings on probability distributions, fluctuation spectra, and effective transmission rates.

Contribution

It introduces a detailed numerical analysis of an SIR model on dynamical networks, linking network structure to epidemic dynamics and quantifying screening effects.

Findings

PDFs of infected fraction fit gamma functions

Network effects can be absorbed by rescaling infection rates

Derived relation between transmission rate and neighbor correlation

Abstract

In this work we performed a numerical study of an epidemic model that mimics the endemic state of whooping cough in the pre-vaccine era. We considered a stochastic SIR model on dynamical networks that involve local and global contacts among individuals and analyzed the influence of the network properties on the characterization of the quasi-stationary state. We computed probability density functions (PDF) for infected fraction of individuals and found that they are well fitted by gamma functions, excepted the tails of the distributions that are q-exponentials. We also computed the fluctuation power spectra of infective time series for different networks. We found that network effects can be partially absorbed by rescaling the rate of infective contacts of the model. An explicit relation between the effective transmission rate of the disease and the correlation of susceptible individuals with their infective nearest neighbours was obtained. This relation quantifies the known screening of infective individuals observed in these networks. We finally discuss the goodness and limitations of the SIR model with homogeneous mixing and parameters taken from epidemiological data to describe the dynamic behaviour observed in the networks studied.