Optimal control of deterministic and stochastic Eco-epidemic food adulteration model
In this paper, we develop a deterministic and stochastic mathematical model to study the effect of contaminated foods on human health by spreading media awareness. A predator–prey SI model with media-induced response function is considered. In the deterministic case, the model has three equilibria:...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2024-03-01
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| Series: | Results in Control and Optimization |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666720723001388 |
| _version_ | 1797259650238775296 |
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| author | Shivani Khare Kunwer Singh Mathur Krishna Pada Das |
| author_facet | Shivani Khare Kunwer Singh Mathur Krishna Pada Das |
| author_sort | Shivani Khare |
| collection | DOAJ |
| description | In this paper, we develop a deterministic and stochastic mathematical model to study the effect of contaminated foods on human health by spreading media awareness. A predator–prey SI model with media-induced response function is considered. In the deterministic case, the model has three equilibria: trivial, disease-free, and endemic. While the endemic equilibria exist for low media impact provided R0>1. Here, the trivial equilibrium is always unstable. However, the disease-free equilibrium exhibits local and global asymptotically stable behavior provided that R0<1. The conditions for the local behavior of endemic equilibrium are also determined along with the existence of Hopf bifurcation. Further, the impact of external interference is studied for the stochastic model. The stochastic model has a unique global positive solution which is ultimately bounded. The stochastic model also demonstrates asymptotic behavior around disease-free and endemic equilibria. Additionally, optimal control theory has been employed to explore deterministic and stochastic optimal control systems in depth. Finally, the analytical results are validated using some numerical simulations. |
| first_indexed | 2024-04-24T23:12:48Z |
| format | Article |
| id | doaj.art-95a892a56bb84bbe8e1e862ca52154dd |
| institution | Directory Open Access Journal |
| issn | 2666-7207 |
| language | English |
| last_indexed | 2024-04-24T23:12:48Z |
| publishDate | 2024-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Control and Optimization |
| spelling | doaj.art-95a892a56bb84bbe8e1e862ca52154dd2024-03-17T07:58:53ZengElsevierResults in Control and Optimization2666-72072024-03-0114100336Optimal control of deterministic and stochastic Eco-epidemic food adulteration modelShivani Khare0Kunwer Singh Mathur1Krishna Pada Das2Department of Mathematics and Statistics, Dr. Harisingh Gour Vishwavidyalaya, Sagar, Madhya Pradesh, 470003, IndiaSchool of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi, 110067, India; Corresponding author.Department of Mathematics, Mahadevananda Mahavidyalaya Barrackpore, Kolkata, IndiaIn this paper, we develop a deterministic and stochastic mathematical model to study the effect of contaminated foods on human health by spreading media awareness. A predator–prey SI model with media-induced response function is considered. In the deterministic case, the model has three equilibria: trivial, disease-free, and endemic. While the endemic equilibria exist for low media impact provided R0>1. Here, the trivial equilibrium is always unstable. However, the disease-free equilibrium exhibits local and global asymptotically stable behavior provided that R0<1. The conditions for the local behavior of endemic equilibrium are also determined along with the existence of Hopf bifurcation. Further, the impact of external interference is studied for the stochastic model. The stochastic model has a unique global positive solution which is ultimately bounded. The stochastic model also demonstrates asymptotic behavior around disease-free and endemic equilibria. Additionally, optimal control theory has been employed to explore deterministic and stochastic optimal control systems in depth. Finally, the analytical results are validated using some numerical simulations.http://www.sciencedirect.com/science/article/pii/S2666720723001388Food adulterationEco-epidemic modelOptimal controlStochastic modelStability analysis |
| spellingShingle | Shivani Khare Kunwer Singh Mathur Krishna Pada Das Optimal control of deterministic and stochastic Eco-epidemic food adulteration model Results in Control and Optimization Food adulteration Eco-epidemic model Optimal control Stochastic model Stability analysis |
| title | Optimal control of deterministic and stochastic Eco-epidemic food adulteration model |
| title_full | Optimal control of deterministic and stochastic Eco-epidemic food adulteration model |
| title_fullStr | Optimal control of deterministic and stochastic Eco-epidemic food adulteration model |
| title_full_unstemmed | Optimal control of deterministic and stochastic Eco-epidemic food adulteration model |
| title_short | Optimal control of deterministic and stochastic Eco-epidemic food adulteration model |
| title_sort | optimal control of deterministic and stochastic eco epidemic food adulteration model |
| topic | Food adulteration Eco-epidemic model Optimal control Stochastic model Stability analysis |
| url | http://www.sciencedirect.com/science/article/pii/S2666720723001388 |
| work_keys_str_mv | AT shivanikhare optimalcontrolofdeterministicandstochasticecoepidemicfoodadulterationmodel AT kunwersinghmathur optimalcontrolofdeterministicandstochasticecoepidemicfoodadulterationmodel AT krishnapadadas optimalcontrolofdeterministicandstochasticecoepidemicfoodadulterationmodel |