Global stability of a transport-related infection model with general incidence rate in two heterogeneous cities

To further understand the effects of travel on disease spread, a transport-related infection model with general incidence rate in two heterogeneous cities is proposed and analyzed. Some analytical results on the global stability of equilibria (including disease free equilibrium and endemic equilibrium) are obtained. The explicit formula for the basic reproduction number R0 is derived and it is proved to be a threshold for disease spread. To reveal how incidence rate and travel rate influence the disease spread, effects of general incidence rate and travel rate on the dynamics of system are shown via numeric simulations.