A Mathematical Model of Tuberculosis with Passive Immunity and Drug Resistance Effects

Abstract

Despite the enormous progress in prevention and treatment, tuberculosis remains a leading cause of death worldwide. One of the major sources of concern is the drug resistant strain, MDR-TB (Multidrug Resistant Tuberculosis) and XDR-TB (Extensively Drug Resistant Tuberculosis). In this paper we present an extension of the SEIRS epidemiology model of tuberculosis by incorporating passive immunity and MDR-TB. We analyzed the local stability of the disease free equilibrium (DFE) point using the next generation method. The result shows that the DFE point is locallyasymptotically stable whenever and unstable whenever . Furthermore, we constructed a Lyapunov for the global stability of DFE.The resultrevealed that the disease free equilibrium point is globally asymptotically stable whenever . The numerical simulation of the model was carried out to show the effects of drug resistant and passive immunity on the transmission dynamics of Tuberculosis. We conclude that, efficacy of drugs ought to be improved and second line of treatment should be enforce in order to control Tuberculosis.