Optimal control of an infected prey–predator model with fear effect
In this paper, we propose and analyze a prey–predator model with the functional response of Beddington–DeAngelis and the fear effect that have infection only in prey populations. We determine existence criteria of several equilibria, and the stability at different equilibria are presented. We exert...
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2024-04-01
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| Series: | Nonlinear Analysis |
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| Online Access: | https://www.journals.vu.lt/nonlinear-analysis/article/view/35236 |
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| _version_ | 1850226716271706112 |
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| author | Hong Qiu Tianzi Zhang Rumei Hou |
| author_facet | Hong Qiu Tianzi Zhang Rumei Hou |
| author_sort | Hong Qiu |
| collection | DOAJ |
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In this paper, we propose and analyze a prey–predator model with the functional response of Beddington–DeAngelis and the fear effect that have infection only in prey populations. We determine existence criteria of several equilibria, and the stability at different equilibria are presented. We exert pesticide control over prey and additional food control over predators, the optimal control is obtained by the Pontryagin maximum principle. We confirm that adding controls to the predator and prey yields better results. Further we enrich our analysis with the inclusion of the existence and uniqueness of the optimal control. Finally, some numerical results to illustrate our analysis are presented.
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| format | Article |
| id | doaj-art-efb6a851f20b4e0e9ae8b6a17870b3c9 |
| institution | OA Journals |
| issn | 1392-5113 2335-8963 |
| language | English |
| publishDate | 2024-04-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Nonlinear Analysis |
| spelling | doaj-art-efb6a851f20b4e0e9ae8b6a17870b3c92025-08-20T02:04:59ZengVilnius University PressNonlinear Analysis1392-51132335-89632024-04-0129410.15388/namc.2024.29.35236Optimal control of an infected prey–predator model with fear effectHong Qiu0Tianzi Zhang1Rumei Hou2Civil Aviation University of ChinaCivil Aviation University of ChinaCivil Aviation University of China In this paper, we propose and analyze a prey–predator model with the functional response of Beddington–DeAngelis and the fear effect that have infection only in prey populations. We determine existence criteria of several equilibria, and the stability at different equilibria are presented. We exert pesticide control over prey and additional food control over predators, the optimal control is obtained by the Pontryagin maximum principle. We confirm that adding controls to the predator and prey yields better results. Further we enrich our analysis with the inclusion of the existence and uniqueness of the optimal control. Finally, some numerical results to illustrate our analysis are presented. https://www.journals.vu.lt/nonlinear-analysis/article/view/35236prey–predator systemoptimal controlfear effectstability |
| spellingShingle | Hong Qiu Tianzi Zhang Rumei Hou Optimal control of an infected prey–predator model with fear effect Nonlinear Analysis prey–predator system optimal control fear effect stability |
| title | Optimal control of an infected prey–predator model with fear effect |
| title_full | Optimal control of an infected prey–predator model with fear effect |
| title_fullStr | Optimal control of an infected prey–predator model with fear effect |
| title_full_unstemmed | Optimal control of an infected prey–predator model with fear effect |
| title_short | Optimal control of an infected prey–predator model with fear effect |
| title_sort | optimal control of an infected prey predator model with fear effect |
| topic | prey–predator system optimal control fear effect stability |
| url | https://www.journals.vu.lt/nonlinear-analysis/article/view/35236 |
| work_keys_str_mv | AT hongqiu optimalcontrolofaninfectedpreypredatormodelwithfeareffect AT tianzizhang optimalcontrolofaninfectedpreypredatormodelwithfeareffect AT rumeihou optimalcontrolofaninfectedpreypredatormodelwithfeareffect |