Mathematical Analysis of a Two-Strain Tuberculosis Model Incorporating Treatment Success, Acquired Drug Resistance, Reactivation, and Reinfection

Tuberculosis remains a major global health challenge, particularly because of the emergence of multidrug-resistant tuberculosis (MDR-TB), which is resistant to key first-line anti-tuberculosis drugs. This study develops a deterministic two-strain tuberculosis model incorporating drug-sensitive tuberculosis (DS-TB), whose causative bacteria remain susceptible to standard first-line treatment, and MDR-TB. The model further incorporates treatment success, acquired drug resistance, effective reactivation flows from a pooled recovered class, and reinfection. The model is shown to be epidemiologically well posed, and an explicit expression for the basic reproduction number is derived using the next-generation matrix approach. The disease-free equilibrium and implicit conditions characterizing endemic equilibria are analyzed mathematically. Sensitivity analysis and numerical simulations examine the influence of transmission, treatment initiation, treatment success, resistance amplification, effective reactivation, and reinfection on tuberculosis dynamics. Under the selected baseline parameter set, reduced treatment success and increased resistance amplification increase the simulated MDR-TB burden. The framework identifies how these mechanisms jointly influence the simulated DS-TB and MDR-TB burdens, providing a mathematical basis for examining integrated tuberculosis-control mechanisms.