Estimating epidemiological parameters of a stochastic differential model of HIV dynamics using hierarchical Bayesian statistics

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: at-risk population exhaustion, lack of access to care, and usage of anti-retroviral therapy (ART) by diagnosed individuals. An extant problem in the mathematical study of this system is deriving parameter estimates due to a portion of the population being unobserved. We approach this problem by looking at the proportional change in the infected subpopulations. 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). Model fit is quantified to determine the best parametric explanation for the observed dynamics in the infected subpopulations. Parameter estimates derived using these methods produce simulations that closely follow the dynamics observed in the data, as well as values that are generally in agreement with prior understanding of transmission and diagnosis rates. Simulations suggest that the undiagnosed population may be larger than currently estimated without significantly affecting the population dynamics.