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Bifurcation and global stability in an eco-epidemic model with refuge

机译：在一个分岔和全球稳定eco-epidemic模型与避难所

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摘要

In this work, we formulate a predator-prey-pathogen model in which the predator is specialist in nature and infected prey can undergo refugia of constant size to avoid predator attack. To investigate the predation effect on the epidemics, we take a situation where the predator eats infected prey only. This is in accordance with the fact that the infected individuals are less active and can be caught more easily. Though it is a well-known fact that consumption of infected prey may harm predator population, the opposite holds in few cases. This leads to a controlled measure of disease prevalence. As predator consumes a particular type of prey species, Holling type II functional response is appropriate. This corroborates to the specialist type of predator. For biological validity of the model, boundedness of the system is studied. The dynamical behavior of the model has been analyzed throughly. Model analysis shows that all the population remains in coexistence when predator consumes the infected preyrather than the susceptible one. The results establish the fact that the effects of refuge used by prey decrease the equilibrium density of susceptible prey population, whereas the opposite holds for infected prey population. However, equilibrium density of predator may decrease or increase by increasing the amount of prey refuge. Global stability of the coexistence equilibrium point is developed by using Li and Muldowney's high-dimensional Bendixson's criterion. Numerical simulations are performed tovalidate our theoretical results.
机译：在这项工作中,我们制定一个predator-prey-pathogen模型中“捕食者”在本质上是专家和感染常数大小的猎物可以接受的聚集地避免捕食者的攻击。捕食对流行病的影响,我们取一个情况下捕食者吃了受感染的猎物只有。受感染的个人不太积极更容易被抓。消费受感染的猎物可能损害的事实捕食者的人口,相反的在几个用例。疾病流行。特定类型的猎物,温和II型功能性反应是适当的。证实专业类型的捕食者。生物模型的有效性,有界性系统的进行了研究。分析了模型的。分析表明,所有的人口仍在共存时,捕食者消耗受感染preyrather比敏感。建立保护区的影响这一事实使用的猎物的平衡密度降低易感人口的猎物,而恰恰相反适用于受感染人群的猎物。平衡捕食者密度可能会减少或通过增加猎物的数量增加的避难所。全球稳定共存的平衡点是由使用李和Muldowney高维本迪克松准则。模拟tovalidate我们执行理论结果。

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