Format

Choose Destination
J Math Biol. 2016 Oct;73(4):787-813. doi: 10.1007/s00285-015-0961-5. Epub 2016 Jan 9.

# On the extinction probability in models of within-host infection: the role of latency and immunity.

### Author information

1
School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC, Australia.
2
School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC, Australia. jamesm@unimelb.edu.au.
3
Melbourne School of Population and Global Health, The University of Melbourne, Parkville, VIC, Australia. jamesm@unimelb.edu.au.
4
Modelling and Simulation, Infection and Immunity Theme, Murdoch Childrens Research Institute, The Royal Children's Hospital, Parkville, VIC, Australia. jamesm@unimelb.edu.au.

### Abstract

Not every exposure to virus establishes infection in the host; instead, the small amount of initial virus could become extinct due to stochastic events. Different diseases and routes of transmission have a different average number of exposures required to establish an infection. Furthermore, the host immune response and antiviral treatment affect not only the time course of the viral load provided infection occurs, but can prevent infection altogether by increasing the extinction probability. We show that the extinction probability when there is a time-dependent immune response depends on the chosen form of the model-specifically, on the presence or absence of a delay between infection of a cell and production of virus, and the distribution of latent and infectious periods of an infected cell. We hypothesise that experimentally measuring the extinction probability when the virus is introduced at different stages of the immune response, alongside the viral load which is usually measured, will improve parameter estimates and determine the most suitable mathematical form of the model.

#### KEYWORDS:

Extinction probability; Immune response; Influenza; Multi-type branching process; Viral dynamics; Within-host model

PMID:
26748917
DOI:
10.1007/s00285-015-0961-5
[Indexed for MEDLINE]