Abstract
Tuberculosis (TB) is a major public health concern in many developing countries. Mycobacterium tuberculosis is a major cause of morbidity and mortality in Africa. Tuberculosis infection is curable but in the cases of incomplete treatment, the remains of Mycobacterium tuberculosis in the human body usually results in the bacterium developing resistant to antibiotics. In this study we developed a model that explains the dynamics of tuberculosis infection in the presence of drug resistance. The basic reproduction number of the model was computed using the next generation matrix approach. The disease free equilibrium and endemic equilibrium were obtained and their stability analysis were carried out. It revealed that they were locally and globally asymptotically stable whenever the reproductive number was less than unity. Numerical simulation of the TB model was conducted and the result revealed that contact rate can reduce or eliminate the sensitive strain and reduce drug resistant of tuberculosis.
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