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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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/950396 |
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| _version_ | 1849412908363022336 |
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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. |
| format | Article |
| id | doaj-art-4c9740c5017e4e2b801c2dac037c4550 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| 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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