Transmission dynamics and applications of HIV/AIDS model with nonlinear testing in the heterosexual and homosexual populations

The unaware HIV-infected population usually bring the cryptic transmission risk in the community. Testing the unaware HIV-infected population becomes a significant approach for controlling cryptic transmission risk of HIV/AIDS, because the testing results provide unaware HIV-infected population with infection statuses and undertaking interventions. To characterize the impacts of HIV testing on cumulative diagnosed scale of HIV/AIDS, we propose a cryptic transmission model of HIV/AIDS with nonlinear testing in the heterosexual and homosexual populations. Theoretically, the basic reproduction number R0 for the total population is calculated by the next generation matrix method, which takes the maximum of the basic reproduction number R0m for the homosexual population, and the basic reproduction number R0f for the heterosexual population. Under different threshold conditions, the globally asymptotic stabilities of disease-free, boundary and endemic equilibrium points are derived, by constructing Lyapunov function and applying the LaSalle’s invariance principle. In other words, when R0m<1 and R0f<1 hold, HIV/AIDS is extinct in the total population. When R0m>1>R0f is valid, HIV/AIDS is prevalent in the homosexual population. When R0f>1>R0m is true, HIV/AIDS is prevalent in the heterosexual population. When R0m>1 and R0f>1 hold, HIV/AIDS is prevalent in the total population. Numerically, the optimal fitting results show that the heterosexual population contribute to the majority of HIV/AIDS epidemics of Fujian Province from 2012 to 2022, and the simulation results for four testing scenarios (testing-free, male-testing, female-testing, male-and-female testing) reveal that HIV testing for undiagnosed male and female populations largely reduces the current infection scale and the cryptic transmission risk. Especially, the enhancement of HIV testing for undiagnosed female population significantly suppresses cumulative diagnosed scale. The prediction results show that, as of the end of 2035, the continuous enhancement of HIV testing for undiagnosed female and male populations contributes to the less cumulative diagnosed scale of HIV/AIDS, and the 95% diagnostic detection objective of Fujian Province will be achieved ahead of schedule.