Incorporating social determinants of health into the mathematical modeling of HIV/AIDS

Currently, it is estimated that 37.6 million people are living with the HIV/AIDS virus worldwide, placing HIV/AIDS among the ten leading causes of death, mostly among low- and lower-middle-income countries. Despite the effective intervention in the prevention and treatment, this reduction did not occur equally among populations, subpopulations and geographic regions. This difference in the occurrence of the disease is associated with the social determinants of health (SDH), which could affect the transmission and maintenance of HIV. With the recognition of the importance of SDH in HIV transmission, the development of mathematical models that incorporate these determinants could increase the accuracy and robustness of the modeling. This article aims to propose a theoretical and conceptual way of including SDH in the mathematical modeling of HIV/AIDS. The theoretical mathematical model with the Social Determinants of Health has been developed in stages. For the selection of SDH that were incorporated into the model, a narrative literature review was conducted. Secondly, we proposed an extended model in which the population (N) is divided into Susceptible (S), HIV-positive (I), Individual with AIDS (A) and individual under treatment (T). Each SDH had a different approach to embedding in the model. We performed a calibration and validation of the model. A total of 31 SDH were obtained in the review, divided into four groups: Individual Factors, Socioeconomic Factors, Social Participation, and Health Services. In the end, four determinants were selected for incorporation into the model: Education, Poverty, Use of Drugs and Alcohol abuse, and Condoms Use. the section "Numerical simulation" to simulate the influence of the poverty rate on the AIDS incidence and mortality rates. We used a Brazilian dataset of new AIDS cases and deaths, which is publicly available. We calibrated the model using a multiobjective genetic algorithm for the years 2003 to 2019. To forecast from 2020 to 2035, we assumed two lines of poverty rate representing (i) a scenario of increasing and (ii) a scenario of decreasing. To avoid overfitting, we fixed some parameters and estimated the remaining. The equations presented with the chosen SDH exemplify some approaches that we can adopt when thinking about modeling social effects on the occurrence of HIV. The model was able to capture the influence of the employment/poverty on the HIV/AIDS incidence and mortality rates, evidencing the importance of SDOH in the occurrence of diseases. The recognition of the importance of including the SDH in the modeling and studies on HIV/AIDS is evident, due to its complexity and multicausality. Models that do not take into account in their structure, will probably miss a great part of the real trends, especially in periods, as the current on, of economic crisis and strong socioeconomic changes