Analysis of the dynamics of phytoplankton nutrient and whooping cough models with nonsingular kernel arising in the biological system

Rajarama Mohan Jena, Snehashish Chakraverty and Subrat Kumar Jena

Chaos, Solitons & Fractals, 2020, vol. 141, issue C

Abstract: In this study, the dynamics of the phytoplankton nutrient and whooping cough models have been examined. Mechanisms of transmission of whooping cough and phytoplankton nutrient models are defined in the Atangana-Baleanu-Caputo (ABC) fractional derivative sense. The first biological system is concerned with the dynamics of phytoplankton–nutrient interaction in the recycling of nutrients, and the second is the modeling of whooping cough in the human population. The essential characteristics of the titled models have been presented, and further, the transmissions of the models defined in the ABC sense are addressed. The concept of fixed point theory is used to derive the existence and uniqueness results of the titled models. Solutions are obtained using the homotopy perturbation Elzaki transform method (HPETM), and numerical results are computed. Graphical analysis of the effect of arbitrary order derivatives has been investigated in detail.

Keywords: Fractional calculus; Atangana-Baleanu derivative; Fixed point theorem; Phytoplankton nutrient model; Whooping cough model; Epidemiology, Perturbation method (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:141:y:2020:i:c:s0960077920307670

DOI: 10.1016/j.chaos.2020.110373

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