A new model for investigating the transmission of infectious diseases in a prey‐predator system using a non‐singular fractional derivative. (16th April 2021)

• Record Type: Journal Article
• Authors: Ghanbari, Behzad
• Other Names: Singh Jagdev guestEditor.; Kumar Devendra guestEditor.; Baleanu Dumitru guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 46:Number 7(2023)
• Page Start: 8106
• Page End: 8125
• Publication Date: 2021-04-16
• Subjects: biological model -- chaos -- computational methods -- equilibrium analysis -- fractional calculus; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7412
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : During past decades, the study of the interaction between predator and prey species has become one of the most exciting topics in computational biology and mathematical ecology. In this paper, we aim to investigate the stability of a diseased model of susceptible, infected prey and predators around an internal steady state. To this end, the fractional derivatives based on the Mittag‐Leffler kernels in the Liouville‐Caputo concept has been taken into consideration. The existence and uniqueness of the acquired solutions to the model are also studied in this paper. In order to investigate the effects of the fractional‐order along with other existing parameters in the model, several possible scenarios have been examined. As it is seen in the proposed graphical simulations, the employed fractional operator is capable of capturing all anticipated theoretical features of the model. The numerical technique employed in this contribution is precise and efficient and can be easily adopted to investigate many fractional‐order models in biology. It is found that new proposed operators of fractional‐order can describe the real‐world phenomena even better than integer‐order differential equations because of their memory‐related properties.