Modeling epidemic in metapopulation networks with heterogeneous diffusion rates.

In this paper, the process of the infectious diseases among cities is studied in metapopulation networks. Based on the heterogeneous diffusion rate, the epidemic model in metapopulation networks is established. The factors affecting diffusion rate are discussed, and the relationship among diffusion rate, connectivity of cities and the heterogeneity parameter of traffic flow is obtained. The existence and stability of the disease-free equilibrium and the endemic equilibrium are analyzed, and epidemic threshold is also obtained. It is shown that the more developed traffic of the city, the greater the diffusion rate, which resulting in the large number of infected individuals; the stronger the heterogeneity of the traffic flow, the greater the threshold of the disease outbreak. Finally, numerical simulations are performed to illustrate the analytical results.