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

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.