Kumar Pushpendra, Baleanu Dumitru, Erturk Vedat Suat, Inc Mustafa, Govindaraj V
Department of Mathematics, National Institute of Technology Puducherry, Karaikal, 609609 India.
Department of Mathematics, Cankaya University, Ankara, Turkey.
Adv Contin Discret Model. 2022;2022(1):11. doi: 10.1186/s13662-022-03684-x. Epub 2022 Jan 29.
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.
我们分析了一个含有时滞的Caputo型分数阶数学模型，该模型包含Beddington-DeAngelis功能反应的感染率，以研究媒介传播的植物流行病的结构。我们通过使用不动点结果证明了给定的时滞数学模型存在唯一的全局解。我们使用Adams-Bashforth-Moulton P-C算法来求解给定的动力学模型。我们对所提出的解给出了一些图形解释。从给定的实际和理论观察中得到了许多新颖的结果。通过使用三维图，我们观察了分数阶变化时图形平坦度的变化。研究了时滞对所提出的植物病害动态的作用以及感染率对易感类和感染类种群的影响。本研究的主要动机是在记忆效应下从分数阶导数的角度研究媒介传播流行病的动态。本研究是分数阶导数在植物流行病学中如何有用的一个例子。具有相等维数的Caputo导数的应用在模型中包含了记忆，这是本研究的主要新颖之处。
