Inference for a stochastic model with application to the within-host dynamics of herpes simplex virus type 2

We develop inference procedures for the Markov/General/infinity queueing model, a stochastic model that arises in a wide variety of fields. In the model, objects arrive at a site according to a Poisson process and depart after an independent and identically distributed residence time. However, observation of the site yields only indicator data recording the occupied or unoccupied state of the site over time. We develop methods of using the indicator data to estimate the arrival rate and residence time distribution of the objects. We develop methods that can be applied when the site is observed either continuously or only at discrete time points. In the latter case, we assume the residence time distribution is exponential. Our procedures use Bayesian inference with Markov chain Monte Carlo techniques.; We apply the model to the study of the dynamics of herpes simplex virus type 2 (HSV-2) within an infected person. HSV-2 is a highly prevalent infection that causes genital herpes and facilitates the transmission of human immunodeficiency virus. We apply the model to data on viral activity at an observable anatomical site (the genital tract) to make inferences about viral activity at an unobservable anatomical site (the nerve cell bodies of the sacral ganglia). Two applications to HSV-2 are presented. In a natural history study, we characterize viral dynamics over the long-term course of the infection. In an application to a clinical trial, we characterize the impact of an antiviral therapy on viral dynamics. These applications demonstrate the methods and contribute to the field of within-host viral dynamic modeling.