The effect of treatment-induced resistance in a two-strain tuberculosis model with age structure and spatial...

Tuberculosis (TB) is a highly contagious chronic infectious disease that, without timely intervention, can lead to severe health consequences or even death. Improper or incomplete treatment often induces the emergence of drug-resistant TB (DR-TB), which greatly complicates disease management and intensifies its public health burden. This paper develops and analyzes a two-strain TB transmission model incorporating age structure during latency, spatial diffusion, and a treatment-induced resistance pathway. Methodologically, we establish the global existence and non-negativity of model solutions and derive explicit expressions for the basic reproduction numbers of the sensitive and resistant strains, as well as for the reproduction number associated with treatment-induced resistance. This study then extends the persistence proof method for single-strain space-age structured models to examine the dynamics of competitive exclusion and persistence between the two strains. Subsequently, we characterize the local and global stability of equilibria using spectral analysis and Lyapunov function methods. Calibrating the model with WHO data for China, we estimate that the basic reproduction number for the sensitive strain exceeds one, and owing to the presence of a treatment-induced resistance pathway, the basic reproduction number for the resistant strain displays two distinct distributions, both of which remain below one. Despite this, theoretical and numerical results demonstrate that DR-TB can persist even when its basic reproduction number is less than one or even zero. Furthermore, our projections indicate that, given the current level of TB control, China is unlikely to achieve the WHO's 2035 incidence reduction target. Despite this, significant improvement in treatment efficacy and reduction of resistance induction risk could make the goal attainable. Moreover, under comparable conditions, the elimination target appears relatively easier to achieve for DR-TB. Our findings suggest that in the absence of treatment-induced resistance, the WHO's DR-TB elimination goal could be reached approximately 2 years earlier. Notably, early increases in DR-TB cases due to improved treatment should be anticipated, underscoring that TB control efforts must not only target existing DR-TB cases but also ensure standardized treatment for drug-sensitive TB (DS-TB) infections; otherwise, treatment-induced resistance in patients will further increase the TB burden.