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A Simple Model of Epidemics with Pathogen Mutation


  • Michelle Girvan
  • Duncan S. Callaway
  • M. E. J. Newman
  • Steven H. Strogatz


We study how the interplay between the memory immune response and pathogen mutation affects epidemic dynamics in two related models. The first explicitly models pathogen mutation and individual memory immune responses, with contacted individuals becoming infected only if they are exposed to strains that are significantly different from other strains in their memory repertoire. The second model is a reduction of the first to a system of difference equations. In this case, individuals spend a fixed amount of time in a generalized immune class. In both models, we observe four fundamentally different types of behavior, depending on parameters: (1) pathogen extinction due to lack of contact between individuals, (2) endemic infection, (3) periodic epidemic outbreaks, and (4) one or more outbreaks followed by extinction of the epidemic due to extremely low minima in the oscillations. We analyze both models to determine the location of each transition. Our main result is that pathogens in highly connected populations must mutate rapidly in order to remain viable.

Suggested Citation

  • Michelle Girvan & Duncan S. Callaway & M. E. J. Newman & Steven H. Strogatz, 2001. "A Simple Model of Epidemics with Pathogen Mutation," Working Papers 01-05-030, Santa Fe Institute.
  • Handle: RePEc:wop:safiwp:01-05-030

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    References listed on IDEAS

    1. Armen A. Alchian, 1950. "Uncertainty, Evolution, and Economic Theory," Journal of Political Economy, University of Chicago Press, vol. 58, pages 211-211.
    2. Blume, L. E. & Bray, M. M. & Easley, D., 1982. "Introduction to the stability of rational expectations equilibrium," Journal of Economic Theory, Elsevier, vol. 26(2), pages 313-317, April.
    3. Blume, Lawrence & Easley, David, 1992. "Evolution and market behavior," Journal of Economic Theory, Elsevier, vol. 58(1), pages 9-40, October.
    4. D. Blackwell & L. Dubins, 2010. "Merging of Opinions with Increasing Information," Levine's Working Paper Archive 565, David K. Levine.
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