A Mathematical Modelling of Tuberculosis Infection Dynamics with effeects of Case detection and Drug Resistance

Abstract

A deterministic mathematical model of tuberculosis incorporating case detection and drug resistance with constant recruitment rate was developed. The population was subdivided into six compartments according to their disease status. The basic reproduction number of the model was obtained using the next generation matrix. The existence of disease free and endemics equilibrium points were shown and the conditions for their stability was also esterblished. The results show that the disease free equilibrium points are locally asymptotically stable if 0 1 R  and globally stable if 0 1 R  . Also the results further show that the endemic equilibrium points are locally asymptotically stable if 0 1 R  and globally stable if 0 1 R  .We obtain the approximate solution of the model using Homotopy Perturbation Methods. The graphical summaries of the solution were carried out and the result show that increase in case detection and sustained treatment can help to reduce transmission of tuberculosis disease