Journal of Mathematical Biology

, Volume 73, Issue 4, pp 787–813 | Cite as

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

  • Ada W. C. Yan
  • Pengxing Cao
  • James M. McCaw


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.


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

Mathematics Subject Classification

92D30 60J70 60J80 



The authors would like to thank Peter Taylor and Sophie Hautphenne for valuable discussions. Ada W. C. Yan is supported by an Australian Postgraduate Award. Pengxing Cao is supported by a National Health and Medical Research Council funded Centre for Research Excellence in Infectious Diseases Modelling to Inform Public Health Policy (1078068). James M. McCaw is supported by an Australian Research Council Future Fellowship (110100250).

Supplementary material

285_2015_961_MOESM1_ESM.pdf (301 kb)
Supplementary material 1 (pdf 300 KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Ada W. C. Yan
    • 1
  • Pengxing Cao
    • 1
  • James M. McCaw
    • 1
    • 2
    • 3
  1. 1.School of Mathematics and StatisticsThe University of MelbourneParkvilleAustralia
  2. 2.Melbourne School of Population and Global HealthThe University of MelbourneParkvilleAustralia
  3. 3.Modelling and Simulation, Infection and Immunity Theme, Murdoch Childrens Research InstituteThe Royal Children’s HospitalParkvilleAustralia

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