The influence of an infectious disease on a prey-predator model equipped with a fractional-order derivative
Abstract In this research, we discuss the influence of an infectious disease in the evolution of ecological species. A computational predator-prey model of fractional order is considered. Also, we assume that there is a non-fatal infectious disease developed in the prey population. Indeed, it is con...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-01-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-020-03177-9 |
| _version_ | 1818591447535845376 |
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| author | Salih Djilali Behzad Ghanbari |
| author_facet | Salih Djilali Behzad Ghanbari |
| author_sort | Salih Djilali |
| collection | DOAJ |
| description | Abstract In this research, we discuss the influence of an infectious disease in the evolution of ecological species. A computational predator-prey model of fractional order is considered. Also, we assume that there is a non-fatal infectious disease developed in the prey population. Indeed, it is considered that the predators have a cooperative hunting. This situation occurs when a pair or group of animals coordinate their activities as part of their hunting behavior in order to improve their chances of making a kill and feeding. In this model, we then shift the role of standard derivatives to fractional-order derivatives to take advantage of the valuable benefits of this class of derivatives. Moreover, the stability of equilibrium points is studied. The influence of this infection measured by the transmission rate on the evolution of predator-prey interaction is determined. Many scenarios are obtained, which implies the richness of the suggested model and the importance of this study. The graphical representation of the mathematical results is provided through a precise numerical scheme. This technique enables us to approximate other related models including fractional-derivative operators with high accuracy and efficiency. |
| first_indexed | 2024-12-16T10:12:35Z |
| format | Article |
| id | doaj.art-5cb129394ca643f289da4a1351d7710d |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-16T10:12:35Z |
| publishDate | 2021-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-5cb129394ca643f289da4a1351d7710d2022-12-21T22:35:32ZengSpringerOpenAdvances in Difference Equations1687-18472021-01-012021111610.1186/s13662-020-03177-9The influence of an infectious disease on a prey-predator model equipped with a fractional-order derivativeSalih Djilali0Behzad Ghanbari1Laboratoire d’Analyse Non Linéaire et Mathématiques Appliquées, Université de TlemcenDepartment of Basic Science, Kermanshah University of TechnologyAbstract In this research, we discuss the influence of an infectious disease in the evolution of ecological species. A computational predator-prey model of fractional order is considered. Also, we assume that there is a non-fatal infectious disease developed in the prey population. Indeed, it is considered that the predators have a cooperative hunting. This situation occurs when a pair or group of animals coordinate their activities as part of their hunting behavior in order to improve their chances of making a kill and feeding. In this model, we then shift the role of standard derivatives to fractional-order derivatives to take advantage of the valuable benefits of this class of derivatives. Moreover, the stability of equilibrium points is studied. The influence of this infection measured by the transmission rate on the evolution of predator-prey interaction is determined. Many scenarios are obtained, which implies the richness of the suggested model and the importance of this study. The graphical representation of the mathematical results is provided through a precise numerical scheme. This technique enables us to approximate other related models including fractional-derivative operators with high accuracy and efficiency.https://doi.org/10.1186/s13662-020-03177-9Predator-prey modelInfected preyHunting cooperationFractional calculus |
| spellingShingle | Salih Djilali Behzad Ghanbari The influence of an infectious disease on a prey-predator model equipped with a fractional-order derivative Advances in Difference Equations Predator-prey model Infected prey Hunting cooperation Fractional calculus |
| title | The influence of an infectious disease on a prey-predator model equipped with a fractional-order derivative |
| title_full | The influence of an infectious disease on a prey-predator model equipped with a fractional-order derivative |
| title_fullStr | The influence of an infectious disease on a prey-predator model equipped with a fractional-order derivative |
| title_full_unstemmed | The influence of an infectious disease on a prey-predator model equipped with a fractional-order derivative |
| title_short | The influence of an infectious disease on a prey-predator model equipped with a fractional-order derivative |
| title_sort | influence of an infectious disease on a prey predator model equipped with a fractional order derivative |
| topic | Predator-prey model Infected prey Hunting cooperation Fractional calculus |
| url | https://doi.org/10.1186/s13662-020-03177-9 |
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