Global stability analysis and optimal control problem arise from tuberculosis transmission model with monitored treatment

Abstract

In this paper, we discussed a Tuberculosis model by incorporating monitored treatment intervention and applying optimal control theory to analyze the optimal intervention for TB. Optimal control strategy aims to minimize both the disease burden and the intervention cost. The optimal control problem is derived analytically using the Pontryagin Maximum Principle. Analysis of the model shows that disease-free equilibrium is globally asymptotically stable if the controlled reproduction number is smaller than one and unstable if it is larger than one. Our numerical experiments show that implementation of monitored treatment should be given in the early spread of TB to avoid high cost of intervention. Furthermore, a better quality of treatment will give a lower cost for TB prevention.