Skip to main content

Advertisement

SpringerLink
Log in

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

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Anderson, R. M., & May, R. M. (1979). Population biology of infectious diseases. I. Nature, 280, 361–367.

    Article  Google Scholar 

  • Berec, L., Angulo, E., & Courchamp, F. (2007). Multiple Allee effects and population management. Trends Ecol. Evol., 22, 185–191.

    Article  Google Scholar 

  • Bessa-Gomes, C., Legendre, S., & Clobert, J. (2004). Allee effects, mating systems and the extinction risk in populations with two sexes. Ecol. Lett., 7, 802–812.

    Article  Google Scholar 

  • Busenberg, S., & van den Driessche, P. (1990). Analysis of a disease transmission model in a population with varying size. J. Math. Biol., 28, 257–270.

    Article  MathSciNet  MATH  Google Scholar 

  • Castillo-Chavez, C., & Huang, W. (1995). The logistic equation revisited: the two-sex case. Math. Biosci., 128, 299–316.

    Article  MATH  Google Scholar 

  • Caswell, H., & Weeks, D. E. (1986). Two-sex models: chaos, extinction, and other dynamic consequences of sex. Am. Nat., 128, 707–735.

    Article  Google Scholar 

  • Courchamp, F., Berec, L., & Gascoigne, J. (2008). Allee effects in ecology and conservation. Oxford: Oxford Univ. Press.

    Book  Google Scholar 

  • Dieckmann, U. (2002). Adaptive dynamics of pathogen-host interactions. In U. Dieckmann, J. A. J. Metz, M. W. Sabelis, & K. Sigmund (Eds.), Adaptive dynamics of infectious diseases (pp. 39–59). Cambridge: Cambridge Univ. Press.

    Chapter  Google Scholar 

  • Diekmann, O., & Kretzschmar, M. (1991). Patterns in the effects of infectious diseases on population growth. J. Math. Biol., 29, 539–570.

    Article  MathSciNet  MATH  Google Scholar 

  • Gao, L. Q., & Hethcote, H. W. (1992). Disease transmission models with density-dependent demographics. J. Math. Biol., 30, 717–731.

    Article  MathSciNet  MATH  Google Scholar 

  • Gascoigne, J., Berec, L., Gregory, S., & Courchamp, F. (2009). Dangerously few liaisons: a review of mate-finding Allee effects. Popul. Ecol., 51, 355–372.

    Article  Google Scholar 

  • Getz, W. M., & Pickering, J. (1983). Epidemic models: thresholds and population regulation. Am. Nat., 121, 892–898.

    Article  Google Scholar 

  • Hadeler, K. P., Waldstätter, R., & Wörz-Busekros, A. (1988). Models for pair formation in bisexual populations. J. Math. Biol., 26, 635–649.

    Article  MathSciNet  MATH  Google Scholar 

  • Hardy, C. M., Hinds, L. A., Kerr, P. J., Lloyd, M. L., Redwood, A. J., Shellam, G. R., & Strive, T. (2006). Biological control of vertebrate pests using virally vectored immunocontraception. J. Reprod. Immunol., 71, 102–111.

    Article  Google Scholar 

  • Hilker, F. M. (2010). Population collapse to extinction: the catastrophic combination of parasitism and Allee effect. Journal of Biological Dynamics, 4, 86–101.

    Article  MathSciNet  Google Scholar 

  • Hilker, F. M., Langlais, M., & Malchow, H. (2009). The Allee effect and infectious diseases: extinction, multistability, and the (dis-)appearance of oscillations. Am. Nat., 173, 72–88.

    Article  Google Scholar 

  • Iannelli, M., Martcheva, M., & Milner, F. A. (2005). Gender-structured population modeling. Philadelphia: SIAM.

    Book  MATH  Google Scholar 

  • Jaenike, A. (1996). Suboptimal virulence of an insect-parasitic nematode. Evolution, 50, 2241–2247.

    Article  Google Scholar 

  • Knell, R. J., & Webberley, K. M. (2004). Sexually transmitted diseases of insects: distribution, evolution, ecology and host behaviour. Biol. Rev., 79, 557–581.

    Article  Google Scholar 

  • Kokko, H., & Morrell, L. J. (2005). Mate guarding, male attractiveness, and paternity under social monogamy. Behav. Ecol., 16, 724–731.

    Article  Google Scholar 

  • Kramer, A. M., Dennis, B., Liebhold, A. M., & Drake, J. M. (2009). The evidence for Allee effects. Popul. Ecol., 51, 341–354.

    Article  Google Scholar 

  • Lindström, J., & Kokko, H. (1998). Sexual reproduction and population dynamics: the role of polygyny and demographic sex differences. Proc. R. Soc. Lond. B, 265, 483–488.

    Article  Google Scholar 

  • Little, S. (2001). Reproduction and breeding management in cats. Vet. Med., 96, 549–555.

    MathSciNet  Google Scholar 

  • Lockhart, A. B., Thrall, P. H., & Antonovics, J. (1996). Sexually transmitted diseases in animals: ecological and evolutionary implications. Biol. Rev., 71, 415–471.

    Article  Google Scholar 

  • McCallum, H., Barlow, N., & Hone, J. (2001). How should pathogen transmission be modelled? Trends Ecol. Evol., 16, 295–300.

    Article  Google Scholar 

  • Miller, T. E. X., & Inouye, B. D. (2011). Confronting two-sex demographic models with data. Ecology, 92, 2141–2151.

    Article  Google Scholar 

  • Møller, A. P., & Birkhead, T. R. (1992). A pairwise comparative method as illustrated by copulation frequency in birds. Am. Nat., 139, 644–656.

    Article  Google Scholar 

  • O’Keefe, K. J., & Antonovics, J. (2002). Playing by different rules: the evolution of virulence in sterilizing pathogens. Am. Nat., 159, 597–605.

    Article  Google Scholar 

  • Parvinen, K. (2005). Evolutionary suicide. Acta Biotheor., 53, 241–264.

    Article  Google Scholar 

  • Pugliese, A. (1990). Population models for diseases with no recovery. J. Math. Biol., 28, 65–82.

    Article  MathSciNet  MATH  Google Scholar 

  • Rankin, D. J., & Kokko, H. (2007). Do males matter? The role of males in population dynamics. Oikos, 116, 335–348.

    Article  Google Scholar 

  • Shuster, S. M., & Wade, M. J. (2003). Mating systems and strategies. Princeton: Princeton Univ. Press.

    Google Scholar 

  • Sloan, D. B., Giraud, T., & Hood, M. E. (2008). Maximized virulence in a sterilizing pathogen: the anther-smut fungus and its co-evolved hosts. J. Evol. Biol., 21, 1544–1554.

    Article  Google Scholar 

  • Thrall, P. H., & Antonovics, J. (1997). Polymorphism in sexual versus non-sexual disease transmission. Proc. R. Soc. Lond. B, 264, 581–587.

    Article  Google Scholar 

  • Tobin, P. C., Robinet, C., Johnson, D. M., Whitmire, S. L., Bjørnstad O. N., & Liebhold, A. M. (2009). The role of Allee effects in gypsy moth, Lymantria dispar (L.), invasions. Popul. Ecol., 51, 373–384.

    Article  Google Scholar 

  • Vynnycky, E., & White, R. G. (2010). An introduction to infectious disease modelling. Oxford: Oxford Univ. Press.

    Google Scholar 

Download references

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.

Author information

Authors and Affiliations

  1. Department of Biosystematics and Ecology, Institute of Entomology, Biology Centre ASCR, Branišovská 31, 37005, České Budějovice, Czech Republic

    Luděk Berec

  2. Institute of Mathematics and Biomathematics, Faculty of Science, University of South Bohemia, Branišovská 31, 37005, České Budějovice, Czech Republic

    Luděk Berec

  3. Department of Mathematics and Computer Science, Valparaiso University, 1900 Chapel Drive, Valparaiso, IN, 46383, USA

    Daniel Maxin

Authors
  1. Luděk Berec
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daniel Maxin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Luděk Berec.

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-012-9802-5

Keywords

Search

Navigation