Stochastic Theory of Early Viral Infection: Continuous versus Burst Production of Virions

Viral production from infected cells can occur continuously or in a burst that generally kills the cell. For HIV infection, both modes of production have been suggested. Standard viral dynamic models formulated as sets of ordinary differential equations can not distinguish between these two modes of viral production, as the predicted dynamics is identical as long as infected cells produce the same total number of virions over their lifespan. Here we show that in stochastic models of viral infection the two modes of viral production yield different early term dynamics. Further, we analytically determine the probability that infections initiated with any number of virions and infected cells reach extinction, the state when both the population of virions and infected cells vanish, and show this too has different solutions for continuous and burst production. We also compute the distributions of times to establish infection as well as the distribution of times to extinction starting from both a single virion as well as from a single infected cell for both modes of virion production.Author Summary: The dynamics of HIV infection and treatment has been extensively studied using ordinary differential equation models. Recent work on HIV transmission has suggested that most sexually transmitted infections are started by a single virus or infected cell. This observation coupled with the fact that successful HIV transmission only occurs in 1 per 100 to 1 per 1000 coital acts suggests that early events in infection are stochastic. Here we develop a stochastic model of HIV infection and use it to characterize the dynamics of early infection when virus is released from cells either continuously or in a burst. We show that these mechanisms of viral production produce different early dynamics, with different probabilities of extinction and different distributions of time to establish infection. In deterministic models, these modes of viral production are indistinguishable.