Epidemic Spreading on Metapopulation Networks with Finite Carrying Capacity

In this study, we formulate and analyze a susceptible–infected–susceptible (SIS) dynamic on metapopulation networks, where each node has a finite carrying capacity and the motion of individuals is modulated by vacant space at the destination. We obtain that the vacancy-dependent mobility pattern results in various asymptotic population distributions on heterogeneous metapopulation networks. The resulting population distributions have remarkable impact on the behavior of SIS dynamics. We show that, for the given total number of individuals, higher heterogeneity in population distributions facilitates epidemic spreading in terms of both a smaller epidemic threshold and larger macroscopic incidence. Moreover, we analytically obtain a sufficient condition that the disease-free equilibrium becomes unstable and an endemic state arises. Contrary to the absence of an epidemic threshold in the standard diffusion case without excluded-volume effects, the finite carrying capacity induces a nonzero epidemic threshold under certain conditions in the limit of infinite network sizes with an unbounded maximum degree. Our analytical results agree well with numerical simulations.