Ecoepidemiological model and analysis of prey-predator system
type: Item
instance of: scholarly article
title: Ecoepidemiological model and analysis of prey-predator system
zbMATH Open document ID: 1499.92062
DOI: 10.1155/2021/6679686
author: Abayneh Fentie Bezabih
author: Geremew Kenassa Edessa
author: Koya Purnachandra Rao
published in: Journal of Applied Mathematics
publication date: 2021-06-22T00:00:00Z
review text: Summary: In this paper, the prey-predator model of five compartments is constructed with treatment given to infected prey and infected predator. We took predation incidence rates as functional response type II, and disease transmission incidence rates follow simple kinetic mass action function. The positivity, boundedness, and existence of the solution of the model are established and checked. Equilibrium points of the models are identified, and local stability analyses of trivial equilibrium, axial equilibrium, and disease-free equilibrium points are performed with the method of variation matrix and the Routh-Hurwitz criterion. It is found that the trivial equilibrium point \(E_o\) is always unstable, and axial equilibrium point \(E_A\) is locally asymptotically stable if \(\beta k- (t_1 +d_2) <0\), \(qp_1k- d_3 (s+k)<0\) and \(qp_3k- (t_2 + d_4)(s+k)<0\) conditions hold true. Global stability analysis of an endemic equilibrium point of the model has been proven by considering the appropriate Lyapunov function. The basic reproduction number of infected prey and infected predators are obtained as \(R_{01}= (qp_1 -d_3)^2k \beta d_3 s^2/(qp_1 - d_3) \{(qp_1 - d_3)^2 ks (t_1 + d_2) +rsqp_2 (kqp_1 - k d_3 - d_3 s)\}\) and \(R_{02}=(qp_1 - d_3) (qp_3 d_3) k+\alpha rsq(kqp_1 - kd_3 - d_3 s)/ (qp_1 - d_3)^2(t_2 + d_4)k\), respectively. If the basic reproduction number is greater than one, then the disease will persist in the prey-predator system. If the basic reproduction number is one, then the disease is stable, and if the basic reproduction number is less than one, then the disease dies out from the prey-predator system. Finally, simulations are done with the help of DEDiscover software to clarify results.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 7362074
Wikidata QID: Q115521425
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/6679686
OpenAlex ID: W3132154412
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description: scientific article; zbMATH DE number 7362074