Modelling and analyzing the transmission dynamics of HIV/AIDS epidemic in China

Based on the considerations of round-trip in the treatment process, this paper presents a mathematical model aimed at studying the dynamic behaviour and epidemiological trends of HIV/AIDS. We first calculate the basic reproduction number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mover><mml:mi>R</mml:mi><mml:mo>̅</mml:mo></mml:mover><mml:mn>0</mml:mn></mml:msub></mml:math> and discuss the stability of equilibrium points and the existence of forward bifurcations, validating the theoretical results through numerical simulations. Subsequently, using cumulative HIV/AIDS case data reported in China, we estimate model parameters using the least squares method, achieving a good fit. Furthermore, sensitivity analyses were performed on the model parameters to explain the dependence of the parameters on the infection variables. Finally, the model is applied to evaluate the control effects of treatment coverage at different stages of infection. The results suggest that reducing HIV/AIDS exposure, improving HIV/AIDS screening, promoting infectious disease treatment and increasing disease prevention awareness are the most effective measures to prevent HIV/AIDS infection.