Mathematical analysis of two-patch model for the dynamical transmission of tuberculosis

The spread of tuberculosis is studied through a two-patch epidemiological model. We assume that susceptible individuals can migrate between the two patches, but not infective individuals. We compute the basic reproduction number R0R0, the disease-free equilibrium, two boundaries endemic equilibria which we define as the existence of the disease in one sub-population while the disease dies out in other sub-population, and the endemic equilibrium when the disease persists in the two sub-populations for specific conditions. We also determine stability criteria for the disease-free equilibrium, boundaries endemic equilibria and the endemic equilibrium. Numerical results are provided to illustrate theoretical results.