title: 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.
authors.affiliation: Theoretical Biology & Biophysics, Los Alamos National Laboratory, Los Alamos, New Mexico, United States of America.
authors.forename: John E
authors.initials: JE
authors.lastname: Pearson
authors.forename: Paul
authors.initials: P
authors.lastname: Krapivsky
authors.forename: Alan S
authors.initials: AS
authors.lastname: Perelson
mesh_terms: D000818:Animals; D019295:Computational Biology; D006678:HIV / Q000502:physiology; D015658:HIV Infections / Q000209:etiology / Q000821:virology; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological; D016097:Simian Acquired Immunodeficiency Syndrome / Q000209:etiology / Q000821:virology; D015302:Simian Immunodeficiency Virus / Q000502:physiology; D013269:Stochastic Processes; D013997:Time Factors; D019562:Viral Load; D014771:Virion / Q000502:physiology*; D014777:Virus Diseases / Q000209:etiology* / Q000821:virology*; D014779:Virus Replication