Dynamical Analysis of Nutrient-Phytoplankton-Zooplankton Model with Viral Disease in Phytoplankton Species under Atangana-Baleanu-Caputo Derivative

Songkran Pleumpreedaporn, Chanidaporn Pleumpreedaporn, Jutarat Kongson, Chatthai Thaiprayoon, Jehad Alzabut and Weerawat Sudsutad
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Songkran Pleumpreedaporn: Department of Mathematics, Faculty of Science and Technology, Rambhai Barni Rajabhat University, Chanthaburi 22000, Thailand
Chanidaporn Pleumpreedaporn: Department of Mathematics, Faculty of Science and Technology, Rambhai Barni Rajabhat University, Chanthaburi 22000, Thailand
Jutarat Kongson: Research Group of Theoretical and Computation in Applied Science, Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand
Chatthai Thaiprayoon: Research Group of Theoretical and Computation in Applied Science, Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand
Jehad Alzabut: Deparment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
Weerawat Sudsutad: Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand

Mathematics, 2022, vol. 10, issue 9, 1-33

Abstract: A mathematical model of the nutrient-phytoplankton-zooplankton associated with viral infection in phytoplankton under the Atangana-Baleanu derivative in Caputo sense is investigated in this study. We prove the theoretical results for the existence and uniqueness of the solutions by using Banach’s and Sadovskii’s fixed point theorems. The notion of various Ulam’s stability is used to guarantee the context of the stability analysis. Furthermore, the equilibrium points and the basic reproduction numbers for the proposed model are provided. The Adams type predictor-corrector algorithm has been applied for the theoretical confirmation to establish the approximate solutions. A variety of numerical plots corresponding to various fractional orders between zero and one are presented to describe the dynamical behavior of the fractional model under consideration.

Keywords: Atangana-Baleanu-Caputo fractional derivative; fixed-point theorems; numerical simulations; nutrient-phytoplankton-zooplankton; Ulam-Hyres stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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