The complete classification for dynamics in a homosexually-transmitted disease model.

A sexually-transmitted disease model for two strains of pathogen in a one-sex, heterogeneously-mixing population was proposed by Li et al. in (J Math Biol 10:1037-1052, 1986). The sufficient and necessary conditions for coexistence and the sufficient conditions for stability of the boundary equilibria were provided. This paper will present a thorough classification of dynamics for this model in terms of the first and second so called reproductive numbers of infection in strains I and J. This classification not only solves a conjecture proposed in (Li et al., J Math Biol 10:1037-1052, 1986) but also gives the sufficient and necessary conditions for the competitive exclusion.