Is the HIV epidemic over? Investigating population dynamics using Bayesian methodology to estimate epidemiological parameters for a system of stochastic differential equations

Abstract

Current estimates of the HIV epidemic indicate a decrease in the incidence of the disease in the undiagnosed subpopulation over the past 10 years. However, a lack of access to care has not been considered when modeling the population. Populations at high risk for contracting HIV are twice as likely to lack access to reliable medical care. In this paper, we consider three contributors to the HIV population dynamics: susceptible pool exhaustion, lack of access to care, and usage of anti-retroviral therapy (ART) by diagnosed individuals. We consider the change in the proportion of undiagnosed individuals as the parameter in a simple Markov model. We obtain conservative estimates for the proportional change of the infected subpopulations using hierarchical Bayesian statistics. The estimated proportional change is used to derive epidemic parameter estimates for a system of stochastic differential equations (SDEs). Epidemic parameters are modified to capture the dynamics of each of the three contributors, as well as all their possible combinations. Model fit is quantified to determine the best explanation for the observed dynamics in the infected subpopulations.\n\nAuthor summaryUsing a combination of statistics and mathematical modeling, we look at some possible reasons for the reported decrease in the number of undiagnosed people living with HIV. One possibility is that the population of people at significant risk to contract HIV is being depleted (susceptibles). This might happen if significant risk for HIV infection occurs in small percentages of the overall population. Another possibility is that infected individuals lack access to care in some regions due to poverty or other cause. In this case we have to question the accuracy of the estimated size of that population. Finally, most diagnosed individuals report being on medication that reduces their viral load. This greatly reduces their chance to transmit HIV to susceptible individuals. We also combine these possibilities and look at the best explanation for the infected population size.