Two-strain Tuberculosis Transmission Model under Three Control Strategies

Abstract

In 1997, Castillo-Chavez and Feng developed a two-strain tuberculosis (TB) model, which is typical TB and resistant TB. Castillo-Chavez and Feng’s model was then subsequently developed by Jung et al. (2002) by adding two control variables. In this work, Jung et al.’s model was modified by introducing a new control variable so that there are three controls, namely chemoprophylaxis and two treatment strategies, with the application of three different scenarios related to the objective functional form and control application. Pontryagin maximum principle was applied to derive the differential equations system as a condition that must be satisfied by the optimal control variables. Furthermore, the fourth-order Runge-Kutta method was exploited to determine the numerical solution of the optimal control problem. In this numerical solution, it is shown that the controls treated on TB transmission model provide a good effect because latent and infected individuals are decreasing, and the number of individuals that is treated effectively is increasing.