Modelling the transmission dynamics and optimal control strategies for HIV infection in China.

In order to end the AIDS epidemic by 2030 that was put forward by the Joint United Nations Programme on HIV/AIDS in 2014, China needs to take more effective measures to achieve the three 90% goals (90-90-90). We establish a compartmental model to study the dynamics of HIV transmission with control strategies. The analytical results show the existence and stability of the disease-free equilibrium and endemic equilibrium. An optimal control model is constructed to evaluate the impacts of control measures. The simulation results show that the optimal control strategy proposed in this work can eradicate AIDS by 2030. The cost-effectiveness analysis indicates that the cost of the control strategy that combines screening for latent individuals and enhancing education for unaware infected individuals is the lowest. Our findings can provide guidance for public health authorities on effective mitigation strategies to achieve the goals proposed by the United Nations Program on HIV/AIDS.