Epidemic thresholds and disease dynamics in metapopulations: the role of network geometry and human mobility

TL;DR

This paper investigates how network structure and human mobility influence epidemic thresholds and disease spread in metapopulations, using analytical formulas and simulations across various network geometries.

Contribution

It derives epidemic threshold formulas for star and cycle networks and explores their implications for disease dynamics in complex network structures.

Findings

Star networks share epidemic thresholds with fully connected networks under certain conditions.

Cycle networks exhibit different epidemic thresholds than star networks.

Simulations support theoretical predictions across various network geometries.

Abstract

We calculate epidemic thresholds and investigate the dynamics of a disease in a networked metapopulation model. To study the specific role of mobility levels and network geometry, we utilize the SIR-Network model and consider a range of geometric structures. For \emph{star-shaped} networks where all nodes only connect to a center, we obtain the same epidemic threshold formula as previously found for fully connected networks in the case where all nodes have the same infection rate except one. Next, we analyze \emph{cycle-shaped} networks that yield different epidemic thresholds than star-shaped ones. We then analyze more general classes of networks by combining the star, cycle, and other structures, obtaining classes of networks with the same epidemic threshold formulas. We present some conjectures on even more flexible networks and complete our analysis by presenting simulations to explore the epidemic dynamics for the different geometries.