A study on fractional host–parasitoid population dynamical model to describe insect species

Abstract

The parasitoid is a broad evolutionary association of hymenopteran insects which are well‐known as biological control agents. Parasites are different from predators because parasites only take resources from one host, whereas predators eat many preys. The preeminent target of this study is to present a fractional model of host–parasitoid population dynamical system through the Caputo operator. The host–parasitoid population dynamical model is a system of three dimensional coupled differential equations. This research also investigates the possibility for obtaining new chaotic behaviors with singular fractional operator and shows the chaotic behavior at different values of fractional order. Furthermore, two numerical schemes Adam–Bashforth–Moulton and new Toufik–Atangana mechanism were suggested to solve fractional host–parasitoid population numerically. Again, some numerical simulations are perform to assess the efficiency of the newly proposed method. Some attractive illustration is presented through graphically. We strongly believe that the proposed work will open various new doors of investigations toward modeling on parasitoid.

Dynamics of SIQR epidemic model with fractional order derivative

“…We have used the Caputo–Fabrizio operator because of its possession of a nonlocal and nonsingular exponential kernel and is found to be best suited to analyze the dynamics of COVID-19. [30] , [31] , [32] , [33] , [34] , [35] , [36] , [37] , [38] , [39] , [40] The dynamics of COVID-19 (Coronavirus Disease-2019) transmission are described using a fractional order SIQR model. We investigate the disease’s impact using an appropriate mathematical model [SIQR model] in context of the Caputo–Fabrizio fractional differential equation, motivated by early research.…”

Attractive Multistep Reproducing Kernel Approach for Solving Stiffness Differential Systems of Ordinary Differential Equations and SomeError Analysis

“…Therefore, there has become an urgent need for effective numerical algorithms to find accurate solutions for such models especially for large periods of time. This gives us the incentive, in this work, to explore effective accurate solutions [31][32][33][34][35][36][37][38][39]. Motivated by the previous discussion, our study aims to design a novel iterative algorithm to generate an analytical solution to stiff models of ordinary differential equations over a large duration through the use of a multi-step technique.…”

Modeling the dynamics of novel coronavirus (COVID-19) via stochastic epidemic model

“…From all these, it could be noted that the reported studies are based on the deterministic approach, while the nature of the coronavirus follows the stochastic process instead of deterministic. The concept of stochastic modeling was used by many researchers to investigate the dynamics of infectious disease in the real world phenomenon, see for detail [ [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] , [33] , [34] ]. As there is no disease-endemic state in stochastic system, hence, the persistence of the disease cant be found.…”