Impacts of migration and immigration on disease transmission dynamics in heterogeneous populations

Abstract

Population migration and immigration have greatly increased thespread and transmission of many infectious diseases at a regional,national and global scale. To investigate quantitatively andqualitatively the impact of migration and immigration on thetransmission dynamics of infectious diseases, especially inheterogeneous host populations, we incorporate immigration/migrationterms into all sub-population compartments, susceptible andinfected, of two types of well-known heterogeneous epidemic models:multi-stage models and multi-group models for HIV/AIDS and otherSTDs. We show that, when migration or immigration into infectedsub-population is present, the disease always becomes endemic in thepopulation and tends to a unique asymptotically stable endemicequilibrium $P^*.$ The global stability of $P^*$ is establishedunder general and biological meaningful conditions, and the proofutilizes a global Lyapunov function and the graph-theoretictechniques developed in Guo et al. (2008).