Fatal or Harmless: Extreme Bistability Induced by Sterilizing, Sexually Transmitted Pathogens

Abstract

Models of sexually transmitted infections have become a fixture of mathematical epidemiology. A common attribute of all these models is treating reproduction and mating, and hence pathogen transmission, as uncoupled events. This is fine for humans, for example, where only a tiny fraction of sexual intercourses ends up with having a baby. But it can be a deficiency for animals in which mating and giving birth are tightly coupled, and mating thus mediates both reproduction and pathogen transmission. Here, we model dynamics of sterilizing, sexually transmitted infections in such animals, assuming structural consistency between the processes of reproduction and pathogen transmission. We show that highly sterilizing, sexually transmitted pathogens trigger bistability in the host population. In particular, the host population can end up in two extreme alternative states, disease-free persistence and pathogen-driven extinction, depending on its initial state. Given that sterilizing, sexually transmitted infections that affect animals are abundant, our results might implicate an effective pest control tactic that consists of releasing the corresponding pathogens, possibly after genetically enhancing their sterilization power.

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Acknowledgements

This work was assisted by attendance as a Short-term Visitor at the National Institute for Mathematical and Biological Synthesis, an Institute sponsored by the National Science Foundation, the US Department of Homeland Security, and the US Department of Agriculture through the NSF Award #EF-0832858, with additional support from The University of Tennessee, Knoxville. LB acknowledges funding from the Institute of Entomology (Z50070508). D.M. acknowledges funding from Wheat Ridge Ministries—O.P. Kretzmann Grant for Research in the Healing Arts and Sciences. The authors wish to thank the two reviewers for their detailed and helpful reports that improved the exposition of this paper.

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Correspondence to Luděk Berec.

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Berec, L., Maxin, D. Fatal or Harmless: Extreme Bistability Induced by Sterilizing, Sexually Transmitted Pathogens. Bull Math Biol 75, 258–273 (2013). https://doi.org/10.1007/s11538-012-9802-5

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Keywords

  • Disease transmission
  • Mating
  • Population dynamics
  • Population management
  • Sexually transmitted disease