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AN ECO-EPIDEMIOLOGICAL MODEL INVOLVING PREY REFUGE AND PREY HARVESTING WITH BEDDINGTON-DEANGELIS, CROWLEY MARTIN AND HOLLING TYPE II FUNCTIONAL RESPONSES
* 1 , 1 , 1 , 2
1  SRI RAMAKRISHNA MISSION VIDYALAYA COLLEGE OF ARTS AND SCIENCE, COIMBATORE, TAMILNADU ,INDIA
2  Department of Mathematics, United Institute of Technology, Coimbatore, Tamilnadu, India
Academic Editor: Simeone Chianese

Abstract:

This paper represents a three-species food web model based on the interactions between
susceptible prey, infected prey, and predator species. It is considered that in the absence of
predator species and prey species grow logistically. Predators consume susceptible and infected
prey in the form of Crowley-Martin and Beddington-DeAngelis Functional Responses. Also,
infected prey consumes susceptible prey in the form of Holling type II interactions.
Positiveness, boundedness and positive invariance are examined. All biologically feasible
equilibrium points are investigated. The local stability of these equilibrium points and their
global stability are analysed by suitable Lyapunov functions of these equilibrium points.
Finally, numerical solutions are analyzed according to our findings.

Keywords: Eco epidemiological model, Crowley martin functional response, Beddington DeAngelis response, Stability, Equilibrium.
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