Impact of density-dependent migration flows on epidemic outbreaks in heterogeneous metapopulations

TL;DR

This paper explores how density-dependent migration influences epidemic spread in complex networks, revealing that migration patterns can either contain or facilitate outbreaks depending on nonlinear diffusion rates.

Contribution

It introduces a nonlinear diffusion model for migration in metapopulations and analyzes its impact on epidemic dynamics, highlighting counterintuitive effects of migration on outbreak locations.

Findings

Strengthening migration from populous areas can contain early epidemic spread.

Epidemic outbreaks may not always occur in the most populated areas, depending on diffusion rate exponent.

Analytical results quantify the impact of migration on epidemic thresholds.

Abstract

We investigate the role of migration patterns on the spread of epidemics in complex networks. We enhance the SIS-diffusion model on metapopulations to a nonlinear diffusion. Specifically, individuals move randomly over the network but at a rate depending on the population of the departure patch. In the absence of epidemics, the migration-driven equilibrium is described by quantifying the total number of individuals living in heavily/lightly populated areas. Our analytical approach reveals that strengthening the migration from populous areas contains the infection at the early stage of the epidemic. Moreover, depending on the exponent of the nonlinear diffusion rate, epidemic outbreaks do not always occur in the most populated areas as one might expect.