HIV/AIDS hidden transmission model with HIV testing and contact tracing in an SID community.

HIV testing and contact tracing facilitate early detection of HIV/AIDS infections for interrupting the hidden transmission. In this study, a susceptible-undiagnosed-diagnosed transmission model with testing and contact tracing is proposed in heterosexual and homosexual populations. The basic reproduction number, the heterosexual-transmission and homosexual-transmission reproduction numbers of the transmission model are derived by the next generation matrix method. The optimal-fitting results present that the basic reproduction number of Fujian 2012-2022 HIV/AIDS epidemics ranges from 1.93 to 2.74 by phases, which is consistent with the heterosexual-transmission reproduction number. The optimal fittings and the global sensitivity analysis show that the transmission risk mainly originates from the heterosexual contacts. The transmission risk assessments and the 2023-2035 tendency predictions are performed for HIV/AIDS prevalence in Fujian Province by scenarios. The numerical simulation results point out that the decrease of female-to-male transmission rate, the decline of proportion of active diagnosed population, and the reduction of the awareness delay, are the main contributors for declining HIV/AIDS prevalence. The 2023-2035 tendency predictions of Fujian Province reveal that, when the awareness delay is fixed, the rising trends of the infection scales caused by the transmission rates are more significant than those caused by the proportion of active diagnosed population. According to the transmission risk assessments and the tendency prediction results, several suggestions are provided to the policymakers for curbing the HIV/AIDS transmission in Fujian Province.