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

Sze-Bi Hsu ； I-Fang Sun

《Tamkang Journal of Mathematics》 52卷1期 (2021/03) Pp. 1-18

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

摘要

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 populations. 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 β_1β_2 plane (See Figure 3) and the second one is in R^((0))-line (See Figure 4).

關鍵字

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