Keywords: HIV, Bayesian, Stochastic Differential Equations, SDE, epidemiology, population modeling, population dynamics
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 project, we consider three contributors to the HIV population dynamics: susceptible pool exhaustion, lack of access to care, and increased prevalence of preventative medication. We consider the change in the proportion of undiagnosed and diagnosed individuals as the parameters in two first-order autoregressive models. We obtain a conservative estimate for these parameters using hierarchical Bayesian statistics. A system of stochastic differential equations is used to obtain probability estimates for the trend in the population. The proportional change is used to derive epidemic parameter estimates in an extended model. Finally, we present likelihoods and analytic solutions for the three hypothesized contributors to the trend in HIV incidence.