On Epidemic Spreading under Mobility on Networks

TL;DR

This paper develops a deterministic model for epidemic spread influenced by mobility on networks, analyzing equilibria and stability, and demonstrating the impact of network structure and mobility on disease dynamics.

Contribution

It introduces a continuum limit model for coupled epidemic-mobility dynamics on networks, analyzing equilibria and stability with Lyapunov methods.

Findings

Existence of disease-free and endemic equilibria under different conditions

Mobility influences the stability and behavior of epidemic spread

Model accurately approximates stochastic dynamics in finite populations

Abstract

We study a coupled epidemic-mobility model in which, at each time, individuals move in a network of spatially-distributed regions (sub-populations) according to a Continuous Time Markov Chain (CTMC) and subsequently interact with the local sub-population according to an SIS model. We derive a deterministic continuum limit model describing these interactions. We prove the existence of a disease-free equilibrium and an endemic equilibrium under different parameter regimes and establish their (almost) global asymptotic stability using Lyapunov techniques. For the stability of disease-free equilibrium, we also deduce some simple sufficient conditions which highlight the influence of mobility on the behavior of the SIS dynamics. Finally, we numerically illustrate that the derived model provides a good approximation to the stochastic model with a finite population and also demonstrate the influence of the graph structure on the transient performance.