Abstract

A MATHEMATICAL MODEL OF TUBERCULOSIS WITH EFFECTS OF IMMUNITY AND DRUG RESISTANCE

* U. Garba, N. G. A Abimbola, S. Z. Idris, N. I. Sulaimanand and A. M. Abdullahi

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Abstract In this Paper, a Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model was modified to determine the effect of immunity and drug resistance on the transmission dynamics of tuberculosis. The equilibrium point was found and its stability was investigated. By analyzing the model, we found a threshold value the basic reproduction number and the existence of the disease free equilibrium point. The disease free equilibrium point of the model is locally stable since basic reproduction number , which was obtained from the numerical simulation of the model. The Global stability analysis was obtained and shows that it is globally asymptotically stable. Numerical analysis for the model is done and demonstrated that in the case of patients with both active tuberculosis and MDR tuberculosis, both strains will be gradually eliminated from the population.

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