Modeling and Control for HIV/AIDS Transmission in China Based on Data from 2004 to 2016

HIV is one of the major life-threatening viruses that are spreading in the People's Republic of China (China for short). A susceptible-exposed in the latent stage-infectious (SEI) model is established to sketch the evolution of epidemic. The basic reproduction number is defined. By constructing Lyapunov function, globally asymptotical stabilities of the disease-free and endemic equilibria are given. Then, optimal control theory is applied in HIV/AIDS epidemic. Precaution, screening, and treatment of control variables are introduced and a new model with control is established. Through the HIV/AIDS data in China, all parameters involved in SEI model are analyzed and parts of them are estimated. Further, by control model, optimal strategy is obtained. Results show that the precaution and treatment are the major contributors to preventing and controlling HIV/AIDS epidemic.