Dynamics of a community transmission model with HIV detection

The prompt and massive detection of the community population with HIV is beneficial to the early diagnosis and helps to determine the main tendency of HIV/AIDS transmission from the perspective of public health and policy makers. In this study, an SIDMA (Susceptible–Infected–Diagnosed–Monitored–AIDS) compartmental model with HIV detection is proposed by using Holling type II functional response. The slow average handling time in HIV detection is taken into account. We first derive the basic reproduction number of the SIDMA model using the next generation matrix method. Then, the global stabilities for disease-free equilibrium point, and boundary equilibrium point are proved under moderate conditions. The research results show that the threshold of global stabilities increases with the monitoring rate. Alternatively, given that the average handling time of HIV detection is fast enough, the research results explore that the underestimation for the threshold of the global stabilities usually exists. This study reveals that positive medical interventions for the community population with HIV improve the life quality through the enhancement of the monitoring rate, also finds that prevalence situation of the community population with HIV is under control.