The dynamics of tuberculosis transmission model with different genders

The dynamics of tuberculosis transmission model with different genders are to be established and studied. The basic regeneration numbers <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mn>0</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mi>F</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mi>M</mml:mi></mml:msub></mml:math> are to be defined, where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mi>F</mml:mi></mml:msub></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mi>M</mml:mi></mml:msub></mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mn>0</mml:mn></mml:msub><mml:mo><</mml:mo><mml:mn>1</mml:mn></mml:math>. 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mn>0</mml:mn></mml:msub><mml:mo>></mml:mo><mml:mn>1</mml:mn></mml:math>, 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.