A Host-Parasite System with Multiple Parasite Strains and Superinfection Revisited: The Global Dynamics.
Acta Biotheor 2020;
68:201-225. [PMID:
31471828 DOI:
10.1007/s10441-019-09359-7]
[Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2019] [Accepted: 08/19/2019] [Indexed: 10/26/2022]
Abstract
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.
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