Global Stability Analysis and Optimal Control of a Harvested Ecoepidemiological Prey Predator Model with Vaccination and Taxation

We propose an ecoepidemiological prey predator model, where selective harvest effort on predator population is considered. Vaccination and taxation are introduced as control instruments, which are utilized to control number of susceptible prey population and protect predator population from overexpl...

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Main Authors: Chao Liu, Qingling Zhang, Jinna Li
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/950396
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author Chao Liu
Qingling Zhang
Jinna Li
author_facet Chao Liu
Qingling Zhang
Jinna Li
author_sort Chao Liu
collection DOAJ
description We propose an ecoepidemiological prey predator model, where selective harvest effort on predator population is considered. Vaccination and taxation are introduced as control instruments, which are utilized to control number of susceptible prey population and protect predator population from overexploitation, respectively. Conditions which influence nonnegativity and boundedness of solutions are studied. Global stability analysis around disease-free equilibrium is discussed based on robust Bendixson criterion, which is theoretically beneficial to studying coexistence and interaction mechanism of population within harvested ecoepidemiological system. By using Pontryagin’s maximum principle, an optimal control strategy is derived to maximize the total discounted net economic revenue to society as well as protect prey population from infectious disease. Numerical simulations are carried out to show the consistency with theoretical analysis.
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institution Kabale University
issn 1085-3375
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language English
publishDate 2013-01-01
publisher Wiley
record_format Article
series Abstract and Applied Analysis
spelling doaj-art-4c9740c5017e4e2b801c2dac037c45502025-08-20T03:34:18ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/950396950396Global Stability Analysis and Optimal Control of a Harvested Ecoepidemiological Prey Predator Model with Vaccination and TaxationChao Liu0Qingling Zhang1Jinna Li2Institute of Systems Science, Northeastern University, Shenyang 110004, ChinaInstitute of Systems Science, Northeastern University, Shenyang 110004, ChinaShenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110004, ChinaWe propose an ecoepidemiological prey predator model, where selective harvest effort on predator population is considered. Vaccination and taxation are introduced as control instruments, which are utilized to control number of susceptible prey population and protect predator population from overexploitation, respectively. Conditions which influence nonnegativity and boundedness of solutions are studied. Global stability analysis around disease-free equilibrium is discussed based on robust Bendixson criterion, which is theoretically beneficial to studying coexistence and interaction mechanism of population within harvested ecoepidemiological system. By using Pontryagin’s maximum principle, an optimal control strategy is derived to maximize the total discounted net economic revenue to society as well as protect prey population from infectious disease. Numerical simulations are carried out to show the consistency with theoretical analysis.http://dx.doi.org/10.1155/2013/950396
spellingShingle Chao Liu
Qingling Zhang
Jinna Li
Global Stability Analysis and Optimal Control of a Harvested Ecoepidemiological Prey Predator Model with Vaccination and Taxation
Abstract and Applied Analysis
title Global Stability Analysis and Optimal Control of a Harvested Ecoepidemiological Prey Predator Model with Vaccination and Taxation
title_full Global Stability Analysis and Optimal Control of a Harvested Ecoepidemiological Prey Predator Model with Vaccination and Taxation
title_fullStr Global Stability Analysis and Optimal Control of a Harvested Ecoepidemiological Prey Predator Model with Vaccination and Taxation
title_full_unstemmed Global Stability Analysis and Optimal Control of a Harvested Ecoepidemiological Prey Predator Model with Vaccination and Taxation
title_short Global Stability Analysis and Optimal Control of a Harvested Ecoepidemiological Prey Predator Model with Vaccination and Taxation
title_sort global stability analysis and optimal control of a harvested ecoepidemiological prey predator model with vaccination and taxation
url http://dx.doi.org/10.1155/2013/950396
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AT jinnali globalstabilityanalysisandoptimalcontrolofaharvestedecoepidemiologicalpreypredatormodelwithvaccinationandtaxation