Bifurcation Control of a Delayed Fractional Mosaic Disease Model for Jatropha curcas with Farming Awareness

Abstract

In this paper, the bifurcation control of a fractional-order mosaic virus infection model for Jatropha curcas with farming awareness and an execution delay is investigated. By analyzing the associated characteristic equation, Hopf bifurcation induced by the execution delay is studied for the uncontrolled system. Then, a time-delayed controller is introduced to control the occurrence of Hopf bifurcation. Our study implies that bifurcation dynamics is significantly affected by the change of the fractional order, the feedback gain and the extended feedback delay provided that the other parameters are fixed. A series of numerical simulations is performed, which not only verifies our theoretical results but also reveals some specific features. Numerically, we find that the Hopf bifurcation gradually occurs in advance with the increase of the fractional order, and there exist extreme points for the feedback gain and the extended feedback delay which can minimize the bifurcation value.

Reliable numerical treatment with Adams and BDF methods for plant virus propagation model by vector with impact of time lag and density

“…The three different models of plant virus propagation by a vector based on the system of ODEs without delay (model A), with delay (model A1), and without delay but including exposed class [E(t)] (model A2) as presented in Equations (1-4), (5)(6)(7)(8), and (9-13) are numerically solved employing the ADM and BDF methods invoking he Mathematica routine with inputs [0, 30] and step size 0.1. Numerical outcomes and The dynamics of plants' natural fatality rate i.e., υ is explored for all four classes S(t), I(t), X(t) and Y(t) using the strength of ADM and BDF methods for scenario 5 of the model A1.…”

“…Several mathematical models have been established to provide a detailed exposition of how to analyze, interpret, and forecast plant pathogenic farming epidemics as a mechanism for formulating and testing crop countermeasures and control measures [1][2][3][4]. A variety of epidemiology models based upon those used mostly in animal or human epidemiology have been created to assess the population ecosystem of viral infections [5][6][7][8][9][10]. The delay differential equations can be used to define relatively different formulations of epidemic proliferation.…”

Artificial intelligence knacks-based stochastic paradigm to study the dynamics of plant virus propagation model with impact of seasonality and delays

“…There have been numerous mathematical models developed to provide a detailed exposition of how to describe, analyze and predict agricultural epidemics of plant pathogens as a mean of developing and testing crop protection tactics and control strategies [5][6][7][8]. There have been a number of epidemiological models developed to analyze the population ecology of viral diseases, based on those used in human or animal epidemiology [9][10][11][12][13][14]. Modeling of host, virus, and vector interactions and their use to evaluate control strategies are discussed [15].…”

On the Dynamics of a Fractional-Order Ebola Epidemic Model with Nonlinear Incidence Rates

“…In recent decades, fractional calculus theory has been applied in many fields such as mechanical and mechanics, viscoelasticity, bioengineering, finance, optimal theory, optical and thermal system, and electromagnetic field theory [1][2][3]. Prior studies have shown that fractional calculus is capable of describing rules and development process of some phenomena in natural science [1].…”

“…In recent decades, fractional calculus theory has been applied in many fields such as mechanical and mechanics, viscoelasticity, bioengineering, finance, optimal theory, optical and thermal system, and electromagnetic field theory [1][2][3]. Prior studies have shown that fractional calculus is capable of describing rules and development process of some phenomena in natural science [1]. In particular, it has been found that the fractional-order differential system has the advantages of simple modeling, clear parameter meaning, and accurate description for some materials and processes with memory and genetic characteristics [4].…”