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Epidemic Models with Heterogeneous Mixing and Treatment

Bulletin of Mathematical Biology volume 70, Article number: 1869 (2008) Cite this article

Abstract

We consider a two-group epidemic model with treatment and establish a final size relation that gives the extent of the epidemic. This relation can be established with arbitrary mixing between the groups even though it may not be feasible to determine the reproduction number for the model. If the mixing of the two groups is proportionate, there is an explicit expression for the reproductive number and the final size relation is expressible in terms of the components of the reproduction number. We also extend the results to a two-group influenza model with proportionate mixing. Some numerical simulations suggest that (i) the assumption of no disease deaths is a good approximation if the disease death rate is small and (ii) a one-group model is a close approximation to a two-group model but a two-group model is necessary for comparing targeted treatment strategies.

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Affiliations

  1. Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada

    Fred Brauer

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  1. Fred Brauer
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Correspondence to Fred Brauer.

Additional information

This research was supported by MITACS and an NSERC Research Grant.

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Brauer, F. Epidemic Models with Heterogeneous Mixing and Treatment. Bull. Math. Biol. 70, 1869 (2008). https://doi.org/10.1007/s11538-008-9326-1

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  • DOI: https://doi.org/10.1007/s11538-008-9326-1

Keywords

  • Epidemic models
  • Final size relation
  • Heterogeneous mixing