A delayed plant disease model with Caputo fractional derivatives

Abstract

We analyze a time-delay Caputo-type fractional mathematical model containing the infection rate of Beddington–DeAngelis functional response to study the structure of a vector-borne plant epidemic. We prove the unique global solution existence for the given delay mathematical model by using fixed point results. We use the Adams–Bashforth–Moulton P-C algorithm for solving the given dynamical model. We give a number of graphical interpretations of the proposed solution. A number of novel results are demonstrated from the given practical and theoretical observations. By using 3-D plots we observe the variations in the flatness of our plots when the fractional order varies. The role of time delay on the proposed plant disease dynamics and the effects of infection rate in the population of susceptible and infectious classes are investigated. The main motivation of this research study is examining the dynamics of the vector-borne epidemic in the sense of fractional derivatives under memory effects. This study is an example of how the fractional derivatives are useful in plant epidemiology. The application of Caputo derivative with equal dimensionality includes the memory in the model, which is the main novelty of this study.

Stability analysis of fractional order modelling of social media addiction

“…The model (4) has been shown positive results whenever the value of ω is decreased gradually from 1. [18,29,41,22,23,25].…”

“…There are numerous approaches in ecology and epidemiology to investigating population and SIR models in the form of systems of ordinary and partial differential equations, difference equations, and fractional-order differential equations. Among them, fractional order differential equations are the most commonly studied because they include various effects and hereditary properties that are important for studying stability characteristics in dynamical and SIR models [18,29,41,22,23]. The phenomenon of fractional order is more realistic as it incorporates the concept of non-integer models, which has been omitted in classical theory.…”

“…In the past few years, many researchers have mainly taken the Caputo type fractional order derivatives instead of Riemann-Liouville derivatives for discussing the results. The reason behind this the Caputo derivatives technique is more appropriate for dealing with physical problems [41,22].…”

Delays in Plant Virus Models and Their Stability

“…Hopf bifurcations can happen in delayed models and have been studied in [20] for an SIRS (susceptible, infective, recovered, susceptible) model and in [17,21] for a plant-virus model. Fractional derivatives have also been introduced in [22,23]. Models have also been introduced for the within-plant interactions with the virus.…”

Numerical Approach for Solving the Fractional Pantograph Delay Differential Equations

“…In recent decades, fractional delay differential equations have had an important role in engineering and natural sciences. Applications of these equations include hydrology, signal processing, control theory, medical sciences, networks, cell biology, climate models, infectious diseases, navigation prediction, circulating blood, population dynamics, oncolytic virotherapy, delayed plant disease model, the body reaction to carbon dioxide, and many others [3][4][5][6].…”