Effects of diffusion rates on epidemic spreads in metapopulation networks

TL;DR

This paper investigates how diffusion rates influence epidemic spreading in metapopulation networks, revealing that diffusion can both suppress and facilitate epidemics depending on the rate, with optimal spreading at intermediate diffusion levels.

Contribution

It demonstrates that diffusion can increase the epidemic threshold in heterogeneous networks, contrasting with previous static network models, and identifies the non-monotonic effect of diffusion on epidemic spread.

Findings

Diffusion suppresses epidemics by increasing the epidemic threshold.

Intermediate diffusion rates maximize epidemic spreading near the threshold.

Diffusion effects differ from static network SIS models.

Abstract

It is often useful to represent the infectious dynamics of mobile agents by metapopulation models. In such a model, metapopulations form a static network, and individuals migrate from one metapopulation to another. It is known that heterogeneous degree distributions of metapopulation networks decrease the epidemic threshold above which epidemic spreads can occur. We investigate the combined effect of heterogeneous degree distributions and diffusion on epidemics in metapopulation networks. We show that for arbitrary heterogeneous networks, diffusion suppresses epidemics in the sense of an increase in the epidemic threshold. On the other hand, some diffusion rates are needed to elicit epidemic spreads on a global scale. As a result of these opposing effects of diffusion, epidemic spreading near the epidemic threshold is the most pronounced at an intermediate diffusion rate. The result that diffusion can suppress epidemics contrasts with that for diffusive SIS dynamics and its variants when individuals are fixed at nodes on static networks.