Mathematical Analysis and Simulation of an Age-Structured Model with Two-Patch and an Uncontrolled Migration: Application to Tuberculosis

Abstract

In this paper, we studied a two-patch age-structured model of tuberculosis in a context where the migration is not controlled. Motivated by the fact that no author has highlighted the impact of migration on the dynamics of transmission of tuberculosis. Each subpopulation is subdivided into five compartments: susceptible; latent, vaccinated, infective and treated. After the determination of the reproductive numbers R(ψ, ρ) and R0(ρ), we established the conditions of the global and local stability of the equilibrium point without disease. It has been shown that there is only one point of endemic equilibrium. Numerical simulations show that uncontrolled migration negatively influences the dynamics of tuberculosis.