Optimizing combination therapy against drug resistance Mycobacterium tuberculosis: a modelling study

Despite the prevalence of co-infection with drug-sensitive and drug-resistant Mycobacterium tuberculosis strains within a single host, the implications of such dual infections remain poorly understood. In this study, we develop a comprehensive within-host model that incorporates both bacterial strains, their mutation dynamics, and cross-reactive immune responses. We analyze the basic reproduction number ( $R_0$ ) and identify its dependence on key parameters, finding that $R_0$ is strongly influenced by the adaptive immune response rate, bacterial fitness cost, and macrophage engulfment rates. Our bifurcation analysis reveals the presence of a backward bifurcation at $R_0=1$ , indicating complex threshold dynamics. Utilizing optimal control theory, we evaluate treatment strategies and demonstrate that a combination therapy with at least 85% efficacy against both strains can effectively control the infection. These findings deepen our understanding of host-pathogen interactions in tuberculosis and provide valuable insights for the development of more effective anti-tuberculosis therapies.