Dynamical behavior of a fractional-order epidemic model for investigating two fear effect functions
Using the Caputo operator, a model for a fractional-order epidemic is developed to investigate the fear effect in a pathogenic environment and vaccination procedure. First, we examine if the proposed model is positive. Next, based on the value of the control reproduction number Rc, we compute both t...
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| Vydáno v: | Results in control and optimization Ročník 16; s. 100474 |
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| Hlavní autoři: | , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier B.V
01.09.2024
Elsevier |
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| ISSN: | 2666-7207, 2666-7207 |
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| Abstract | Using the Caputo operator, a model for a fractional-order epidemic is developed to investigate the fear effect in a pathogenic environment and vaccination procedure. First, we examine if the proposed model is positive. Next, based on the value of the control reproduction number Rc, we compute both the control reproduction and strength numbers and derive the stability criteria of the disease-free equilibrium. In fact, we use the comparison theorem to show that the disease-free equilibrium point is globally asymptotically stable whenever Rc<1. Next, we prove that the solutions of the fractional model exist and are unique. Finally, several numerical simulations are conducted to verify our theoretical results. |
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| AbstractList | Using the Caputo operator, a model for a fractional-order epidemic is developed to investigate the fear effect in a pathogenic environment and vaccination procedure. First, we examine if the proposed model is positive. Next, based on the value of the control reproduction number Rc, we compute both the control reproduction and strength numbers and derive the stability criteria of the disease-free equilibrium. In fact, we use the comparison theorem to show that the disease-free equilibrium point is globally asymptotically stable whenever Rc<1. Next, we prove that the solutions of the fractional model exist and are unique. Finally, several numerical simulations are conducted to verify our theoretical results. |
| ArticleNumber | 100474 |
| Author | Alaoui, Abdesslem Lamrani Thirthar, Ashraf Adnan Abboubakar, Hamadjam Nisar, Kottakkaran Sooppy |
| Author_xml | – sequence: 1 givenname: Ashraf Adnan surname: Thirthar fullname: Thirthar, Ashraf Adnan email: a.a.thirthar@uofallujah.edu.iq organization: Department of Studies and Planning, University of Fallujah, Anbar, Iraq – sequence: 2 givenname: Hamadjam orcidid: 0000-0002-2213-7185 surname: Abboubakar fullname: Abboubakar, Hamadjam email: h.abboubakar@gmail.com organization: Department of Computer Engineering, University Institute of Technology of Ngaoundéré, The University of Ngaoundéré, P.O. Box 455, Ngaoundéré, Cameroon – sequence: 3 givenname: Abdesslem Lamrani surname: Alaoui fullname: Alaoui, Abdesslem Lamrani email: abdesslemalaoui@gmail.com organization: Moulay Ismail university, FST Errachidia, MAIS Laboratory, MAMCS Group, Morocco – sequence: 4 givenname: Kottakkaran Sooppy orcidid: 0000-0001-5769-4320 surname: Nisar fullname: Nisar, Kottakkaran Sooppy email: n.sooppy@psau.edu.sa organization: Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz University, Al Kharj, Saudi Arabia |
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| Keywords | Epidemic Asymptotic stability 92D30 Fear effect Reproduction number 26A33 |
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