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.

Can't live with them, can't live without them? Balancing mating and competition in two-sex populations

“…The second way in which density-and frequencydependence could interact in two-sex populations is through resource competition [17,18] and other antagonistic intersexual interactions such as harassment [19,20] and disease transmission [21]. Competition occurs both within and between the sexes, and several studies have shown sex differences in competitive ability [18,22].…”

Evolutionary suicide through a non-catastrophic bifurcation: adaptive dynamics of pathogens with frequency-dependent transmission

“…Frequency-dependent incidence is routinely assumed for sexually transmitted diseases (e.g. Thrall et al (1993); Thrall and Antonovics (1997); Boots and Sasaki (2003); Berec and Maxin (2013); Bernhauerová and Berec (2015)). It is also believed to be a suitable description of infection process among animals in herds (Diekmann et al (2012); de Jong et al (1995)) and in vector-borne diseases (Thrall et al (1993); Antonovics et al (1995); Thrall et al (1995)).…”

“…The system in (10) is a generalization of the model considered in Berec and Maxin (2013). In Berec and Maxin (2013), the authors investigate an epidemiological model of a partially sterilizing, sexually transmitted disease in which they take into account the fact that in sexually transmitted diseases, host population birth rates and the rate of infection transmission are both mediated by the mating process. Assuming that σ ∈ [0, 1] is the probability of not becoming sterile upon infection and that both partners must be fertile to produce offspring, they arrive at…”

“…The number of biologically meaningful equilibria depends on the precise form of the functions b S and b I . With b S and b I in (11), there is a unique positive equilibriumx, which is globally stable (Berec and Maxin (2013)). Let nowx(α) denote a stable equilibrium of (10b).…”