Drug-sensitivity and passive immunity mathematical epidemiological model for tuberculosis

Abstract

Regardless of many decades of research, the widespread availability of a vaccine and more recently highly visible WHO efforts to promote a unified global control strategy, Tuberculosis remains a leading cause of infectious mortality. In this paper, a Mathematical Model for Tuberculosis Epidemic with Passive Immunity and Drug-Sensitivity is presented. We carried out analytical studies of the model where the population comprises of eight compartments: passively immune infants, susceptible, latently infected with DS-TB. The Disease Free Equilibrium (DFE) and the Endemic Equilibrium (EE) points were established. The next generation matrix method was used to obtain the reproduction number for drug sensitive (???) Tuberculosis. We obtained the disease-free equilibrium for drug sensitive TB which is locally asymptotically stable when ??? < 1 indicating that tuberculosis eradication is possible within the population. We also obtained the global stability of the disease-free equilibrium and results showed that the disease-free equilibrium point is globally asymptotically stable when ??? ≤ 1 which indicates that tuberculosis naturally dies out.