The complete classification for dynamics of an SIS STD model in terms of four parameters (Q984577)

The author studies a nine-dimensional sexually transmitted disease model proposed by \textit{C. Castillo-Chavez} et al. [J. Math. Biol. 35, No.~5, 503--522 (1996; Zbl 0878.92023)]. This model involves two competing species 1 and 2 in a two-sex heterosexually active population that includes a single group of males and two different groups of females. The author determines the first and second reproduction numbers \(R_i\) and \({\mathcal R}_i\) for species \(i=1,2\), respectively. By applying the theory of type-K monotone dynamical system, the author obtained a complete classification for the dynamics of this model through these reproduction numbers. The author claims that this classification not only is different to the classification given by \textit{C. Castillo-Chavez} et al. [SIAM J. Appl. Math. 59, No.~5, 1790--1811 (1999; Zbl 0934.92029)], but can also be easily explained biologically.