Impacts of Migration and Immigration on Disease Transmission Dynamics in Heterogeneous Populations

Population migration and immigration have greatly increased the spread and transmission of many infectious diseases at a regional, national and global scale. To investigate quantitatively and qualitatively the impact of migration and immigration on the transmission dynamics of infectious diseases, especially in heterogeneous host populations, we incorporate immigration/migration terms into all sub-population compartments, susceptible and infected, of two types of well-known heterogeneous epidemic models: multistage models and multi-group models for HIV/AIDS and other STDs. We show that, when migration or immigration into infected sub-population is present, the disease always becomes endemic in the population and tends to a unique asymptotically stable endemic equilibrium P ∗. The global stability of P ∗ is established under general and biological meaningful conditions, and the proof utilizes a global Lyapunov function and the graph-theoretic techniques developed in Guo et al. (2008).