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).
Highlights
Population migrations are occurring at a global scale: mass of migrant workers are moving from rural regions into large cities in developing countries, and immigrants and refugees are moving from developing countries to industrialized countries
We prove that if infected immigrants are allowed into at least one population group, and the contact network among groups is strongly connected, the disease will persists in all population groups: a unique endemic equilibrium P ∗ exists for all feasible parameter values and is globally asymptotically stable
We have studied two classes of epidemic models for the transmission of infectious diseases in heterogeneous populations
Summary
Population migrations are occurring at a global scale: mass of migrant workers are moving from rural regions into large cities in developing countries, and immigrants and refugees are moving from developing countries to industrialized countries. It is shown in these simple models that, if infected immigrants or migrants are allowed into the host population, the disease will always become and remain endemic: a unique endemic equilibrium always exists and is globally asymptotically stable. We prove that, when immigration is present in at least one infected compartment (latent or infectious), the disease will persists in all sub-populations, and a unique endemic equilibrium is globally asymptotically stable in the feasible region.
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