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

Abstract

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.

Predicting the outcomes of treatment to eradicate the latent reservoir for HIV-1

“…Among all parameters that determine outcome, the establishment probability is least understood, as it cannot be measured from viral load dynamics above the limit of detection. Simply because an integrated provirus is replication competent and transcriptionally active does not mean that it will initiate a growing infection: As with all population dynamics, chance events dominate early stages of infection growth (34,54). HIV-1 transcription is itself a stochastic process, governed by fluctuating concentrations of early gene products (55).…”

HIV Transmission

“…Perelson has suggested that mucosal infections by HIV-1, and by analogy SIV, may be extinguished because of stochastic events in the transmission process (Pearson et al 2011). This could be caused by limitations in target cell availability that may be more significant in cervicovaginal mucosa and submucosa than in rectal tissue (Edwards and Morris 1985;Ma et al 2001;Zhang et al 2004;Pudney et al 2005;Miyake et al 2006).…”

“…These hypotheses were proven to be valid in both acute HIV-1 and SIV infection Liu et al 2010;Stone et al 2010). More recently, Perelson and coworkers developed a stochastic model of the early HIV-1 infection (Pearson et al 2011), as opposed to deterministic models, to probe the earliest virus-host events following virus inoculation. They distinguish virus that is released from cells continuously versus in a burst and show that these different mechanisms of virus production lead to substantially different early viral dynamics and different probabilities of virus extinction.…”

Cell-Free Transmission of Human Adenovirus by Passive Mass Transfer in Cell Culture Simulated in a Computer Model

“…Little is known about lytic cell-free transmission of viruses, although cell-free transmission occurs with both nonenveloped and enveloped viruses and is key for clinical efficacy of oncolytic viruses (57,78,111). Theoretical calculations considering the rate of viral production, life span of the producer cell, and neutralizing capacity of antibodies have suggested that the lytic life cycle with large burst sizes promotes survival in the face of antibody attack (51).…”