Key Laboratory of Eco-Environments in Three Gorges Reservoir Region (Ministry of Education), School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China.
Shanxi Key Laboratory of Mathematical Techniques and Big Date Analysis on Disease Control and Prevention, Complex Systems Research Center, Shanxi University, Taiyuan, 030006, People's Republic of China.
Acta Biotheor. 2020 Jun;68(2):201-225. doi: 10.1007/s10441-019-09359-7. Epub 2019 Aug 30.
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 [Formula: see text] is the threshold condition for parasite extinction and the invasion reproduction number [Formula: see text] 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.
在本文中，我们重新研究了 Nowak 和 May（Proc R Soc Lond B 255(1342):81-89, 1994）提出的具有多种寄生虫株和超感染的宿主-寄生虫系统，并放松了其中的两个严格条件来研究其全局动力学。对于具有两种寄生虫株的系统，我们推导出基本繁殖数[Formula: see text]是寄生虫灭绝的阈值条件，入侵繁殖数[Formula: see text]是两种寄生虫株共存的亚阈值条件。对于具有三种寄生虫株的系统，我们惊讶地发现寄生虫自由和共存平衡点的全局稳定性，这与之前的结果不同。此外，对于具有 n 种寄生虫株的系统，我们得到寄生虫自由平衡点的全局渐近稳定性，猜想共存平衡点的全局稳定性的一般结果，并提供两个数值例子来验证我们的猜想。
