Insights into HIV/AIDS transmission dynamics and control in Indonesia — A mathematical modelling study

This paper presented a new deterministic compartmental model of the dynamics of human immunodeficiency virus (HIV) and acquired immunodeficiency syndrome (AIDS). The model included mother-to-child transmission, the effect of treatment delay through saturated treatment, and screening for early case detection. We obtained the effective reproduction number, ℛ_e, for the model with the help of the next-generation matrix method. A closer look at the model's qualitative parts showed that it can reach unique disease-free and endemic equilibrium points when treatment delay is not present. We showed that the disease-free equilibrium is globally asymptotically stable when ℛ_e is less than one and unstable when ℛ_e is greater than one by making use of Lyapunov function. On the other hand, the endemic equilibrium is globally asymptotically stable when ℛ_e is greater than one. We further confronted the model with real data from Indonesia's annual AIDS cases to obtain more realistic quantitative results. Global sensitivity analysis was carried out to identify the model parameters that most influence the transmission dynamics of HIV/AIDS in the community. We also conducted numerical simulations to illustrate the effects of the three key aspects of HIV/AIDS transmission dynamics which were factored into the model. We discovered that stepping up screening for case detection, treatment, and preventing mother-to-child HIV transmission could potentially prevent thousands of HIV/AIDS cases and AIDS-related deaths in Indonesia by 2029.