Stability and Sensitivity Analysis of Treatment and Distancing in a Mathematical Model for Co-existing Drug-Sensitive and Drug-Resistant Tuberculosis Strains in Bangladesh

Abstract

This abstract provides a summary of a study that employs mathematical modeling to analyze a dual-strain tuberculosis (TB) structure in Bangladesh, focusing on the identification of drug-resistant (DR) and drug-susceptible (DS) strains. The model features a distinctive element known as "amplification," which illustrates how insufficient treatment of DR TB can arise from the management of DS TB. Utilizing both analytical and numerical techniques, the research investigates the disease's dynamics and its potential long-term implications. The primary findings indicate that the long-term dynamics of TB within a population are influenced by the basic reproduction numbers for each strain, referred to as R_0 and R_0 r. The disease tends to naturally decline when there are fewer cases compared to a single growth rate. Conversely, if R_0 exceeds both R_0 and one, DR TB will continue to exist while DS TB is eradicated. If R_0 surpasses R_0 and one, both strains will persist together. Additionally, the research conducted an analysis of vulnerability to identify the key factors impacting the disease's transmission rate. It was determined that the transmission rates (β_s and β_r) of both strains significantly influence the progression of the illness. This underscores the necessity for public health initiatives to focus on strategies that minimize interactions between infected and uninfected individuals, such as educating patients on respiratory safety and enhancing ventilation systems. Another critical factor is the treatment rate (τ_s and τ_r). The social implications of this study are considerable, suggesting that an effective approach for nations like Bangladesh is to improve treatment accessibility by lowering costs through universal healthcare. Timely and appropriate treatment of DS TB is the most effective method to mitigate resistance development, while adequate management of DR TB is crucial to prevent its proliferation within the population.