Mathematical modeling of tuberculosis with two strains, seasonality, and age heterogeneity

Tuberculosis (TB) remains a significant global health threat, particularly in the regions with diverse age-specific transmission patterns and increasing drug resistance. To address these challenges, this study establishes a dual-strain model that incorporates both drug-resistant and drug-sensitive strains to investigate how these strains contribute to the dynamics of TB transmission. By integrating age heterogeneity, social interactions, and seasonal variations, the model offers a detailed depiction of TB transmission process, highlighting its inherent complexity across various population groups. We derive the basic reproduction number of the model as the maximum of the two reproduction numbers: one for the drug-resistant strain (R₀^r) and one for the drug-sensitive strain (R₀^s). It is found that the disease-free periodic equilibrium of the system is globally asymptotically stable when R₀=max(R₀^r,R₀^s)<1, in the absence of reinfection. We further explore the competitive dynamics of drug-resistant and drug-sensitive strains under R₀^r>1>R₀^s and R₀^s>1>R₀^r. Using a Markov Chain Monte Carlo (MCMC) algorithm, the model is calibrated with monthly TB infection data from mainland China, enabling the reconstruction of TB transmission dynamics across eight age-specific groups. The study reveals that drug-sensitive tuberculosis strains exhibit more prominent transmission characteristics compared to drug-resistant strains. Moreover, increased vaccination coverage significantly reduces TB prevalence, particularly in younger populations, while reducing contact intensity effectively suppresses TB across all age groups. These findings highlight the role of combining age-structured modeling, strain dynamics, and behavioral interventions, offering implications for the targeted TB control strategies.