Mathematical Models of HIV: Methodologies and Applications

HIV is one of the significant public health threats globally, with approximately 36.9 million people living with HIV and 1.8 million people becoming newly infected in 2017 (WHO fact sheet). To prevent HIV, to decrease its impact and to eventually eliminate this infectious disease; clinical, medical, epidemiological, economic, and modeling studies have been conducted in the last 30 years. In this study, we explore the mathematical modeling studies where HIV has been examined to understand the dynamics and spread of the disease as well as to improve HIV prevention. We surveyed HIV modeling literature, summarized primary modeling methodologies, and briefly discussed relevant studies. For each study included in this paper, we presented their modeling method, interventions included, target populations, implementation process, key results, and insights. Two most widely used modeling methodologies for HIV are Bernoulli process models and dynamic compartmental models similar to other infectious diseases. These methodologies have been discussed in detail in this paper. Other modeling methodologies included Markov models, agent-based simulation models, and discrete-event simulation models. Many studies focused on risk populations such as heterosexual (HET), men who have sex with men (MSM), people who inject drugs (PWID) and jail inmates. We included the cost-effectiveness studies where HIV prevention and treatment interventions and strategies are compared concerning their costs and benefits. In this survey, we provided a summary of existing modeling literature as well as suggestions for future studies. We concluded that application of modeling tools for HIV presents excellent opportunities for both decision-makers and public health policymakers while predicting the future of this disease, establishing the most cost-effective prevention strategies and evaluating possibilities for the elimination of HIV.