Mathematical analysis of tuberculosis models with differential infectivity, general contact rates, migration and staged progression

Abstract

study covers four fundamental features of tuberculosis dynamics (variable contact rates, differential infectivity, migration and staged progression. The first model under consideration covers the general contact rates and differential infectivity. The second model explores migration and staged progression. In this model, the spread of tuberculosis is studied through a two-patch epidemiological s stem SE1...En1. The study proves that when the basic reproduction ratio is less than unity in the models, the disease-free equilibrium is globally asymptotically stable and when the basic reproduction ratio is greater than unity, a unique endemic equilibrium exists and happens to be globally asymptotically stable under certain conditions. Direct and indirect Lyapunov methods as well as LaSalles invariant set principle are used to investigate the stability of endemic equilibria. Numerical simulations are provided to illustrate the theoretical results.