Fatmawati, .- and Ahmadin, .- (2018) Mathematical modelling of Tuberculosis in a logistically growing human population with optimal control. World Journal of Modelling and Simulatio, 14 (2018). pp. 1745-7233. ISSN 1746-7233

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Abstract

Tuberculosis (TB) is a common deadly infectious disease caused mainly by Mycobacterium tuberculosis. Approximately, one-third of the world’s population is infected by TB. Therefore, the effectiveness of treatment and control strategies to reduce the spread of TB is still needed. In this paper, we proposed and analyzed a mathematical modelling of TB transmission considering logistically growing human population. The model also incorporates TB prevention and anti-TB treatment efforts as control strategies to minimize the number of latent and infectious populations. For model without controls, we obtain the basic reproduction number which determines the stability of the equilibriums of the model. The disease free equilibrium is locally asymptotically stable whenever the reproduction number is less than unity. Using the Pontryagin Maximum Principle, the optimal control theory is then deduced analytically. Numerical simulations are further conducted to confirm the effectiveness of the optimal treatments. According to the simulation results, the combination TB prevention and anti-TB treatment give better result in term minimizing the number of the latent and infected populations. However, as shown by the numerical results, the anti-TB treatment strategy is more effective than TB prevention if we use only one control.

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