Modeling and Analysis of Fractional Order Logistic Equation Incorporating Additive Allee Effect

Authors

  • Preety Kalra Department of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University, Phagwara, Punjab, 144402, India https://orcid.org/0000-0003-0720-8384
  • Nisha Malhotra Department of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University, Phagwara, Punjab, 144402, India https://orcid.org/0000-0002-8899-3283

DOI:

https://doi.org/10.37256/cm.5120243183

Keywords:

logistic growth, single species, additive Allee effect, Caputo derivative, fractional order differential equation

Abstract

This study investigates the logistic model of a single species incorporating the additive Allee effect using Caputo fractional order differential equations. The Allee effect describes a positive correlation between individual fitness and population density at low densities. Populations subjected to the strong Allee effect can move towards extinction when their population is below a critical level. This study calculates the threshold level of the population suffering from the strong Allee effect. Various published studies are showing that fractional order models are more appropriate for explaining real-world phenomena than ordinary integer-order systems; therefore, this study involves the use of the Caputo fractional order derivative. Single-species models have been extensively used in mathematical biology, such as insect control, optimal biological resource planning, epidemic avoidance and control, and cell growth regulation. This study can help save vulnerable species from extinction and eliminate unwanted species by subjecting them to a strong Allee effect using artificial strategies.

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Published

2024-01-27

How to Cite

1.
Kalra P, Malhotra N. Modeling and Analysis of Fractional Order Logistic Equation Incorporating Additive Allee Effect. Contemp. Math. [Internet]. 2024 Jan. 27 [cited 2024 Jun. 17];5(1):380-401. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/3183