In this paper, we revisit a host–parasite system with multiple parasite strains and superinfection proposed by Nowak and May (Proc R Soc Lond B 255(1342):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 $$R_0$$ R 0 is the threshold condition for parasite extinction and the invasion reproduction number $$R_i^j\ (i,j=1,2,i\ne j)$$ R i j ( i , j = 1 , 2 , 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.

中文翻译：

---

重新审视具有多种寄生虫菌株和双重感染的宿主-寄生虫系统：全球动态

在本文中，我们重新审视了由 Nowak 和 May (Proc R Soc Lond B 255(1342):81-89, 1994) 提出的具有多种寄生虫菌株和双重感染的宿主-寄生虫系统，并研究了当我们放松这两个其中假设了严格的条件。对于具有两个寄生虫品系的系统，我们推导出基本繁殖数$$R_0$$R 0 是寄生虫灭绝的阈值条件，入侵繁殖数$$R_i^j\ (i,j=1,2,i \ne j)$$ R ij ( i , j = 1 , 2 , i ≠ j ) 是两种寄生虫共存的亚阈值条件。对于具有三个寄生虫菌株的系统，我们惊讶地发现无寄生虫和共存平衡的全局稳定性，这与之前的结果不同。此外，对于具有 n 个应变的系统，