Modeling the Impact of Prompt and Advanced Drug Treatment on Multidrug Resistant Tuberculosis

ABSTRACT

In this study, a mathematical model for tuberculosis (TB) transmission that incorporates prompt and advanced drug treatment strategies is formulated and analysed. The model describes the interaction between susceptible and infected, and multidrug‐resistant (MDR‐TB) populations. Fundamental properties of the model, including the existence, uniqueness, positivity, and boundedness of the solution are established. The equilibrium points are calculated. The basic reproduction number is computed using the next‐generation matrix. The local and global stability of the disease‐free equilibrium point are also analyzed. It is proved that the disease‐free equilibrium point is locally and globally asymptotically stable whenever . A sensitivity analysis is conducted to find the parameters that mainly influence the transmission of TB. Sensitivity analysis is performed to identify the parameters that are most sensitive to transmission of the disease. On the other hand, the early and advanced treatments significantly reduce the transmission rate. The numerical simulations are carried out using the MATLAB ode45 solver, and a comparison between the RK4 and NSFD schemes is presented to prove the validity of the dynamics of the model.