Stochastic Modeling of Viral Reproductive Cycle: Study of Viral and Cell Extinction

Although viral dynamics is typically modeled using ordinary differential equations, a natural way to address the phenomena of viral persistence and host cell survival is to use stochastic models of viral reproduction. Here we present a study of viral and substrate cell extinction and their dependence on viral production rate for two simple stochastic models of viral reproduction that differ in the method of viral release: one accounts for viral bursting, in which the release of viruses is instantaneous after cell lesion, the other for viral budding, in which new viral particles are released from infected cells gradually. We show that for both viral release mechanisms, simulation of continuous-time Markov chain versions of the stochastic models is the most accurate but also time-consuming way to obtain the results, and that traditional diffusion approximation methods lead to serious discrepancies in extinction probabilities and mean times. We then propose a modified stochastic differential equation approach that achieves a significant improvement in simulation speed while maintaining accuracy.