Competition of Two Host Species for a Single-Limited Resource Mediated by Parasites

Authors

  • Sze-Bi Hsu National Tsing Hua University, Taiwan
  • I-Fang Sun Department of Nature Resources and Environmental studies, National Dong Hwa University, Hualien,Taiwan

DOI:

https://doi.org/10.5556/j.tkjm.52.2021.4016

Keywords:

multi-host, mathematical model, parasite, competition, single-limited resource, chemostat, epidemics models, infective population, susceptible population, locally asymptoti- cally stability of equilibrium

Abstract

In this paper we consider a mathematical model of two host species competing for a single -limited resource mediated by parasites. Each host population is divided into susceptible and infective population. We assume that species 1 has the lowest break-even concentration with respect to nutrient, when there is no parasite. Thus species 1 is a superior competitor that outcompetes species 2. When parasites present, the competitive outcome is determined by the contact rate of the superior competitor. We analyze the model by finding the conditions for the existence of various equilibria and doing their stability analysis. Two bifurcation diagrams are presented. The first one is in $\beta_1$-$\beta_2$ plane (See Figure 3) and the second one is in $R^{(0)}$-line (See Figure 4).

References

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H. L. Smith and P. E. Waltman, The Theory of Chemostat : dynamics of microbial competition, Volume 13. Cambridge university press 1995.

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Published

2021-01-31

How to Cite

Hsu, S.-B., & Sun, I.-F. (2021). Competition of Two Host Species for a Single-Limited Resource Mediated by Parasites. Tamkang Journal of Mathematics, 52(1), 1-18. https://doi.org/10.5556/j.tkjm.52.2021.4016