Abstract

In this paper, we revisit a host–parasite system with multiple parasite strains and superinfection proposed by Nowak and May :81–89, 1994), and study its global dynamics when we relax the two strict conditions assumed therein. As for system with two parasite strains, we derive that the basic reproduction number $$R_0$$ is the threshold condition for parasite extinction and the invasion reproduction number $$R_i^j\ $$ is the subthreshold condition for coexistence of two parasite strains. As for system with three parasite strains, we are surprised to discover the global stability of parasite-free and coexistence equilibrium, which is distinct from the previous result. Furthermore, for system with n strains, we obtain the global asymptotical stability of the parasite-free equilibrium, conjecture a general result on the global stability of coexistence equilibrium and provide two numerical examples to testify our conjecture.