Mathematical Analysis of Tuberculosis Transmission Model with Multidrug and Extensively Drug-resistant Incorporating Chemoprophylaxis Treatment

Abstract

Tuberculosis has remained the principal cause of mortality worldwide, and one of the major sources of concern is drug-resistant TB. The increasing emergence of extensively drug-resistant and multidrug-resistant TB has further increased the TB epidemic. In this current work, we suggest a model to study the transmission of TB with extensively drug-resistant and multidrug-resistant compartments, incorporating chemoprophylaxis treatment. In the theoretical analysis, the concept of the next-generation matrix and the Jacobian method are applied to obtain a formula that states the reproductive number. The existence of endemic and disease-free equilibrium points was checked, and their stability has been analyzed using the Lyapunov method. The qualitative-based analysis indicated the local asymptotic stability of the disease-free-state for R0 1, whereas the endemic state is globally asymptotically stable if R0 1. Moreover, sensitivity analysis was carefully done using normalized forward sensitivity, and numerical simulation was carried out. Based on the results of numerical simulation and sensitivity analysis, chemoprophylaxis treatment was found to drastically minimize the progression of exposed individuals to infectious classes and also reduce the progression to extensively drug-resistant and multidrug-resistant classes, which decreases disease transmission.

Keywords

• mathematical modeling
• extensively drug-resistant
• numerical simulation
• sensitivity analysis
• equilibrium point