Williams, B., Carruthers, J., Gillard, J. J. et al. (5 more authors) (2024) The reproduction number and its probability distribution for stochastic viral dynamics. Journal of the Royal Society. Interface, 21 (210). 20230400. ISSN 1742-5689
Abstract
We consider stochastic models of individual infected cells. The reproduction number, R, is understood as a random variable representing the number of new cells infected by one initial infected cell in an otherwise susceptible (target cell) population. Variability in R results partly from heterogeneity in the viral burst size (the number of viral progeny generated from an infected cell during its lifetime), which depends on the distribution of cellular lifetimes and on the mechanism of virion release. We analyse viral dynamics models with an eclipse phase: the period of time after a cell is infected but before it is capable of releasing virions. The duration of the eclipse, or the subsequent infectious, phase is non-exponential, but composed of stages. We derive the probability distribution of the reproduction number for these viral dynamics models, and show it is a negative binomial distribution in the case of constant viral release from infectious cells, and under the assumption of an excess of target cells. In a deterministic model, the ultimate in-host establishment or extinction of the viral infection depends entirely on whether the mean reproduction number is greater than, or less than, one, respectively. Here, the probability of extinction is determined by the probability distribution of R, not simply its mean value. In particular, we show that in some cases the probability of infection is not an increasing function of the mean reproduction number.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2024 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. |
Keywords: | viral burst size, reproduction number, eclipse phase, infectious phase, Erlang distribution, stochastic model |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Funding Information: | Funder Grant number BBSRC (Biotechnology & Biological Sciences Research Council) BB/W010755/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 03 Jan 2024 10:55 |
Last Modified: | 07 Feb 2024 16:06 |
Status: | Published |
Publisher: | The Royal Society |
Identification Number: | 10.1098/rsif.2023.0400 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:206955 |