Study on Dynamic Behavior of Tuberculosis Model with Gender and Age-Structure

This paper deals with the dynamics of tuberculosis transmission model with different genders and age structures. The basic reproduction numbers [Formula: see text] are defined, where [Formula: see text] and [Formula: see text] are the basic reproduction number of tuberculosis transmission in female and male populations, respectively. The global stability of the disease-free equilibrium was discussed when [Formula: see text]; The existence, uniqueness and global stability of the endemic equilibrium, and the persistence of the system both were proved when [Formula: see text]. The findings indicate that the tuberculosis dynamical model with different genders and age structures will experience the classical threshold dynamic behaviors, that is, if [Formula: see text], the disease will disappear; while if [Formula: see text], the disease will spread within the population, and eventually lead to a endemic disease. Finally, the theoretical analysis of the model is verified by numerical simulation and we proposed that male infected individuals should be focused on in the prevention and control of tuberculosis in the future.