Impact of the Discrete, Stochastic Nature of Cell-Virus Interactions on the Likelihood of Infection Establishment, Interpretations of Experimental Infectivity Measurements, and Parameter Estimation From Such Measurements

A virus infection can be initiated with very few infectious virions, and as such can become extinct, i.e. stochastically fail to take hold. There are many ways that a fully competent infectious virion, having successfully entered a cell, can fail to cause a productive infection, i.e. one that yields infectious virus progeny. Though many discrete, stochastic mathematical models (DSMs) have been developed and used to estimate an infection's extinction probability, these typically neglect infection failure post viral entry. The DSM presented herein introduces parameter γ ∈(0,1] which corresponds to the probability that a virion's entry into a cell will result in a productive cell infection. We derive an expression for the likelihood of extinction in this DSM, and find that prophylactic therapy with an antiviral acting to reduce γ is best at increasing the extinction probability. Using the DSM, we investigate the difference in the fraction of cells consumed by so-called extinct versus established infections. We show how the number of virus released, not the timing of the release, as previously claimed, affects infection extinction. Using a continuous deterministic mathematical model to represent a virus infection, an inherently stochastic process, could lead to inaccurate estimation of infection parameters. Further, to measure infectivity, methods rely on counting the number of infections a sample can cause. Infections in infectivity assays could become extinct and affect the measurements thereof. This raises the question as to whether parameter estimates are different when taking into account the stochastic nature of infection in infection experiments or in their measurements. Herein, we perform parameter estimation, with a DSM and its mean-field counterpart. Notably, for the DSM, a different pair of parameters are degenerate but biologically reasonable rather than arbitrary bounds can be imposed on the degenerate parameters. We find that the stochastic variability is negligible in the actual viral time course of infection experiments but considerable for the measured viral time course. These findings suggest that stochasticity may not play an important role in infection experiments only in their measurements.