Mathematical model of transmission dynamics of human immune-deficiency virus: A case study for Yunnan, China

• We model an HIV/AIDS epidemic model with 12 compartments.
• We obtain the basic reproductive number and four possible equilibria.
• Dynamic behavior of the model is studied.
• Parameters are chosen to fit the HIV/AIDS data in Yunnan.
• The results are beneficial to the control of HIV/AIDS for Yunnan.

In this paper, we present an HIV/AIDS epidemic model with 12 compartments in Yunnan province, China. The total population is divided into four subgroups: injecting drug users(IDUs), female sex workers (FSWs), clients of FSWs (C) and men who have sex with men (MSM). Due to behavioral change, susceptible people will move into the other susceptible groups. A basic reproduction number R0R0 of the model is established by means of a next generation matrix. It is found that the model is locally as well as globally asymptotically stable at the disease free equilibrium when R0<1R0<1 . If R0>1,R0>1, permanence of HIV/AIDS for the model is studied. Based on HIV/AIDS epidemic data in Yunnan province, parameters are chosen to fit the data. The simulations indicate that Yunnan will have about 140,000 HIV positives, 18,000 AIDS cases unless there are any stronger or more effective control measures by the end of 2015. Sexual transmission is the main mode from 2006–2015. The HIV prevalence rate among men who have sex with men continues to increase more quickly until 2015. If effective measures are taken to reduce the transmission rate, then HIV/AIDS spread in Yunnan can be controlled.