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Variability in a Community-Structured SIS Epidemiological Model

Bulletin of Mathematical Biology volume 77, pages 698–712 (2015)Cite this article

Abstract

We study an SIS epidemiological model of a population partitioned into groups referred to as communities, households, or patches. The system is studied using stochastic spatial simulations, as well as a system of ordinary differential equations describing moments of the distribution of infectious individuals. The ODE model explicitly includes the population size, as well as the variability in infection levels among communities and the variability among stochastic realizations of the process. Results are compared with an earlier moment-based model which assumed infinite population size and no variance among realizations of the process. We find that although the amount of localized (as opposed to global) contact in the model has little effect on the equilibrium infection level, it does affect both the timing and magnitude of both types of variability in infection level.

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Acknowledgments

This material is based upon work supported by the National Science Foundation under Grant No. DMS-0746603 to D.H.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Maine, Orono, ME, 04469, USA

    David E. Hiebeler, Rachel M. Rier, Josh Audibert, Phillip J. LeClair & Anna Webber

  2. School of Computing and Information Science, University of Maine, Orono, ME, 04469, USA

    Josh Audibert

  3. Bangor High School, Bangor, ME, 04401, USA

    Josh Audibert, Phillip J. LeClair & Anna Webber

Authors
  1. David E. Hiebeler
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  2. Rachel M. Rier
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  3. Josh Audibert
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  4. Phillip J. LeClair
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  5. Anna Webber
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Correspondence to David E. Hiebeler.

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Hiebeler, D.E., Rier, R.M., Audibert, J. et al. Variability in a Community-Structured SIS Epidemiological Model. Bull Math Biol 77, 698–712 (2015). https://doi.org/10.1007/s11538-014-0017-9

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  • DOI: https://doi.org/10.1007/s11538-014-0017-9

Keywords

  • Variability
  • Community structure
  • Moment closure
  • Epidemiology
  • Stochastic models