Dynamic analysis and optimal control of HIV/AIDS model considering the first 95% target

Based on the level of awareness of the population, an HIV/AIDS model is developed, which focused on the first 95% plan developed by UNAIDS. The threshold of model and the expressions of the disease‐free equilibrium and the endemic equilibrium are calculated, proving the existence of backward bifurcation. Backward bifurcation is caused by the imperfect protection rate of susceptible population due to education. Using China's actual data for parameter fitting, it is found that new HIV infections are on an upward trend. In response to this phenomenon, publicity and education, condoms, screening, and treatment of infected populations are considered as control measures. It is concluded that publicity and education is the primary strategy. This measure can not only effectively reduce the number of infected populations but also effectively increase the awareness rate of HIV‐infected populations. It is recommended to use condoms and have fewer sexual partners during sexual contact. Numerical simulation verifies that early stage publicity and education are much more important than post‐infection screening and treatment measures.