A Host–Parasite System with Multiple Parasite Strains and Superinfection Revisited: The Global Dynamics

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 d...

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Bibliographic Details
Published in:Acta biotheoretica 2020-06, Vol.68 (2), p.201-225
Main Authors: Liu, Lili, Ren, Xinzhi, Liu, Xianning
Format: Article
Language:English
Subjects:
Animals
Basic Reproduction Number
Coexistence
Computer Simulation
Education
Evolutionary Biology
Global Health
Host-Parasite Interactions
Humans
Models, Biological
Parasites
Parasites - pathogenicity
Parasitic Diseases - parasitology
Parasitic Diseases - transmission
Philosophy
Philosophy of Biology
Regular Article
Superinfection
Superinfection - epidemiology
Superinfection - parasitology
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Summary: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 is the threshold condition for parasite extinction and the invasion reproduction number 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.
ISSN:0001-5342
1572-8358
DOI:10.1007/s10441-019-09359-7