Dynamics of an epidemic model with host migration

Host migration among discrete geographical regions is demonstrated as an important factor that brings about the diffusion and outbreak of many vector–host diseases. In the paper, we develop a mathematical model to explore the effect of host migration between two patches on the spread of a vector–host disease. Analytical results show that the reproduction number ${\mathfrak{R}}_0$ provides a threshold condition that determines the uniform persistence and extinction of the disease. If both the patches are identical, it is shown that an endemic equilibrium is locally stable. It is also shown that a unique endemic equilibrium, which exists when the disease cannot induce the death of the host, is globally asymptotically stable. Finally, two examples are given to illustrate the effect of host migration on the spread of the vector–host disease.