A Mathematical Model of the Transmission Dynamics of Tuberculosis with Exogenous Reinfection in the Infection-Free State

Abstract

In the present work, a perturbation of the model presented by Feng, Castillo-Chávez and Capurro (2000) will be carried out, where the dynamics of tuberculosis transmission will be described, where recovery from the disease will be incorporated. The model will include four epidemiological populations: Susceptible (S), Exposed (E), Infected (I) and Infected with treatment (T). This will allow to know how the interaction that exists with the infected can cause the permanence of the individuals with the disease. For which, its qualitative behavior will be analyzed as its evolution in time of the epidemiological populations for the model by the ordinary differential equations (ODE) and its perturbation to the dalay differential equations (DDE). In this way, it will allow us to know how the parameters influence the spread of the disease at the point free of infection and with a computational extension to evaluate an endemic situation.