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

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.