Infectious diseases can seriously impact dynamics of their host species. In this study, we model and analyze an interaction between a sexually transmitted infection and its animal host population affected by a mate-finding Allee effect. Since mating drives both host reproduction and infection transmission, the Allee effect shapes the transmission rate of the infection which we show takes a saturating form. Our model combining sexually transmitted infections with the mate-finding Allee effect in the host produces quite rich dynamics, including oscillations, several multistability regimes, and infection-induced host extinction. However, many of these complex patterns are restricted to a relatively narrow parameter range. We find that the host extinction occurs at intermediate levels of infection virulence, as well as for Allee effect strengths much lower than when the infection is absent. In both cases, a sequence of events comprising destabilization of an endemic equilibrium, growth of oscillation amplitude, and a heteroclinic bifurcation forms an underlying mechanism. We apply our model to the feline immunodeficiency virus (FIV) in domestic cats.

Department of Ecology Institute of Entomology Biology Centre CAS Branišovská 31 37005 České Budějovice Czech Republic

Department of Mathematics and Statistics Faculty of Science Masaryk University Kotlářská 2 61137 Brno Czech Republic

Institute of Mathematics and Biomathematics Faculty of Science University of South Bohemia Branišovská 1760 37005 České Budějovice Czech Republic