Existence and stability results in a fractional optimal control model for dengue and two-strains of salmonella typhi
Co-infection with dengue and salmonella typhi could lead to devastating consequences, and sometimes even result in deaths. This could lead to tremendous hazards not only to country’s economy but also overloading health-care centers. In this article, a fractional co-infection model for dengue, and tw...
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| Language: | English |
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Elsevier
2025-03-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818125000038 |
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| author | Anum Aish Buhader Mujahid Abbas Mudassar Imran Andrew Omame |
| author_facet | Anum Aish Buhader Mujahid Abbas Mudassar Imran Andrew Omame |
| author_sort | Anum Aish Buhader |
| collection | DOAJ |
| description | Co-infection with dengue and salmonella typhi could lead to devastating consequences, and sometimes even result in deaths. This could lead to tremendous hazards not only to country’s economy but also overloading health-care centers. In this article, a fractional co-infection model for dengue, and two-strains (drug-sensitive and drug-resistant) of salmonella typhi is developed by implementing Caputo fractional derivative. Existence, uniqueness and stability of the model are proved by implementing Arzela Ascoli’s theorem, Banach fixed point theorem and Hyers-Ulam stability criteria, respectively. To control the diseases, control measures namely prevention control against dengue, u1(t), prevention control against drug-sensitive salmonella typhi, u2(t), and prevention control against drug-resistant salmonella typhi, u3(t), are introduced into the considered model. The optimality system for corresponding fractional optimal control problem is illustrated by employing Pontryagin’s maximum principle. The simulations of the model are performed by employing fractional Euler scheme to see the impact of control measures and fractional order on the respective diseases. |
| format | Article |
| id | doaj-art-64d01602e4c4489dbb3c62b988679ddf |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-64d01602e4c4489dbb3c62b988679ddf2025-02-05T04:32:45ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-03-0113101075Existence and stability results in a fractional optimal control model for dengue and two-strains of salmonella typhiAnum Aish Buhader0Mujahid Abbas1Mudassar Imran2Andrew Omame3Department of Mathematics, Government College University Katchery Road, Lahore 54000, PakistanDepartment of Mechanical Engineering Science, Faculty of Engineering and the Built Environment, University of Johannesburg, Johannesburg, South AfricaCollege of Humanities and Sciences, Ajman University, Ajman, P.O. Box 346, United Arab Emirates; Corresponding author.Department of Mathematics, Federal University of Technology, Owerri, Nigeria; Department of Mathematics and Statistics, York University Toronto, CanadaCo-infection with dengue and salmonella typhi could lead to devastating consequences, and sometimes even result in deaths. This could lead to tremendous hazards not only to country’s economy but also overloading health-care centers. In this article, a fractional co-infection model for dengue, and two-strains (drug-sensitive and drug-resistant) of salmonella typhi is developed by implementing Caputo fractional derivative. Existence, uniqueness and stability of the model are proved by implementing Arzela Ascoli’s theorem, Banach fixed point theorem and Hyers-Ulam stability criteria, respectively. To control the diseases, control measures namely prevention control against dengue, u1(t), prevention control against drug-sensitive salmonella typhi, u2(t), and prevention control against drug-resistant salmonella typhi, u3(t), are introduced into the considered model. The optimality system for corresponding fractional optimal control problem is illustrated by employing Pontryagin’s maximum principle. The simulations of the model are performed by employing fractional Euler scheme to see the impact of control measures and fractional order on the respective diseases.http://www.sciencedirect.com/science/article/pii/S2666818125000038DengueDrug-sensitive salmonella typhiDrug-resistant salmonella typhiCo-infectionCaputo fractional derivativeExistence |
| spellingShingle | Anum Aish Buhader Mujahid Abbas Mudassar Imran Andrew Omame Existence and stability results in a fractional optimal control model for dengue and two-strains of salmonella typhi Partial Differential Equations in Applied Mathematics Dengue Drug-sensitive salmonella typhi Drug-resistant salmonella typhi Co-infection Caputo fractional derivative Existence |
| title | Existence and stability results in a fractional optimal control model for dengue and two-strains of salmonella typhi |
| title_full | Existence and stability results in a fractional optimal control model for dengue and two-strains of salmonella typhi |
| title_fullStr | Existence and stability results in a fractional optimal control model for dengue and two-strains of salmonella typhi |
| title_full_unstemmed | Existence and stability results in a fractional optimal control model for dengue and two-strains of salmonella typhi |
| title_short | Existence and stability results in a fractional optimal control model for dengue and two-strains of salmonella typhi |
| title_sort | existence and stability results in a fractional optimal control model for dengue and two strains of salmonella typhi |
| topic | Dengue Drug-sensitive salmonella typhi Drug-resistant salmonella typhi Co-infection Caputo fractional derivative Existence |
| url | http://www.sciencedirect.com/science/article/pii/S2666818125000038 |
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