The classification for dynamics of an STD model

In this paper, a 3(n+1) dimensional sexually transmitted disease model is studied. The model involves two competing strains 1 and 2, where females are divided into n different groups based on their susceptibility to two distinct pathogenic strains. The first and second reproduction numbers Ri,Ri, which have their biological meaning, are defined for strain i,i=1,2, respectively. With the non-degeneracy assumption (H), a complete classification for dynamics of this model in terms of Ri,Ri,i=1,2 is presented, which is based on the theory of type-K monotone dynamical systems.