Dynamics and optimal control for tuberculosis transmission via a data-validated periodic model

China is the third-largest contributor to the global incidence of tuberculosis (TB), and there are significant differences in the prevalence of TB among different age groups. Therefore, it is necessary to study the contribution of adolescents to the transmission of tuberculosis. Given that tuberculosis in mainland China exhibits periodic transmission characteristics, a non-autonomous differential equation model that considers age stage and periodic transmission has been proposed. We derived the basic reproduction number R ₀ of this model and proved the global asymptotic stability of the disease-free equilibrium when R ₀ < 1, as well as the persistence of the disease when R ₀ > 1. We estimated the basic reproduction number R ₀ = 1.18, which indicates that tuberculosis in mainland China is of low endemicity. Sensitivity analysis tells us that the adolescent group has a significant impact on the transmission of tuberculosis and is an indispensable force. Furthermore, we constructed a tuberculosis transmission control model and proposed four optimal control strategies, calculated the strategy-related benefits (ACER) and the incremental benefits between strategies (ICER), and further provided targeted recommendations for controlling tuberculosis transmission among different groups.