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- Publisher
- Springer Journals
- Copyright
- Copyright © Springer Nature B.V. 2019
- Subject
- Philosophy; Philosophy of Biology; Evolutionary Biology
- ISSN
- 0001-5342
- eISSN
- 1572-8358
- DOI
- 10.1007/s10441-019-09359-7
- Publisher site
- See Article on Publisher Site
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 R0\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$R_0$$\end{document} is the threshold condition for parasite extinction and the invasion reproduction number Rij(i,j=1,2,i≠j)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$R_i^j\ (i,j=1,2,i\ne j)$$\end{document} 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.
Journal
Acta Biotheoretica – Springer Journals
Published: Jun 30, 2020