Summary In many chronic conditions, subjects alternate between an active and an inactive state, and sojourns into the active state may involve multiple lesions, infections, or other recurrences with different times of onset and resolution. We present a biologically interpretable model of such chronic recurrent conditions based on a queueing process. The model has a birth–death process describing recurrences and a semi-Markov process describing the alternation between active and inactive states, and can be fit to panel data that provide only a binary assessment of the active or inactive state at a series of discrete time points using a hidden Markov approach. We accommodate individual heterogeneity and covariates using a random effects model, and simulate the posterior distribution of unknowns using a Markov chain Monte Carlo algorithm. Application to a clinical trial of genital herpes shows how the method can characterize the biology of the disease and estimate treatment efficacy.