The dynamics of tuberculosis transmission model with different genders.

Abstract

The dynamics of tuberculosis transmission model with different genders are to be established and studied. The basic regeneration numbers $R_0=R_F+R_M$ are to be defined, where $R_F$ and $R_M$ to be the basic reproduction number of tuberculosis transmission in female and male populations, respectively. The existence and global stability of the disease-free equilibrium was discussed when $R_0<1$. The global dynamic behaviours of the corresponding limit system under some conditions are to be provided, including the existence, uniqueness, and global stability of the disease-free equilibrium and endemic equilibrium. The numerical simulation shows that the endemic equilibrium may be unique and stable when $R_0>1$, and the system will undergo Hopf bifurcation based on some parameter values. Finally, we applied this model to analyse the transmission of tuberculosis in China, estimated the incidence of tuberculosis in China in 2035, and gave the conclusion that controlling the incidence of tuberculosis in male populations could better reduce the incidence of tuberculosis in China.