Dynamics of a fractional order mathematical model for COVID-19 epidemic.

IF 4.1 3区数学 Q1 Mathematics Advances in Difference Equations Pub Date : 2020-01-01 Epub Date: 2020-08-14 DOI:10.1186/s13662-020-02873-w

Zizhen Zhang, Anwar Zeb, Oluwaseun Francis Egbelowo, Vedat Suat Erturk

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Abstract

In this work, we formulate and analyze a new mathematical model for COVID-19 epidemic with isolated class in fractional order. This model is described by a system of fractional-order differential equations model and includes five classes, namely, S (susceptible class), E (exposed class), I (infected class), Q (isolated class), and R (recovered class). Dynamics and numerical approximations for the proposed fractional-order model are studied. Firstly, positivity and boundedness of the model are established. Secondly, the basic reproduction number of the model is calculated by using the next generation matrix approach. Then, asymptotic stability of the model is investigated. Lastly, we apply the adaptive predictor-corrector algorithm and fourth-order Runge-Kutta (RK4) method to simulate the proposed model. Consequently, a set of numerical simulations are performed to support the validity of the theoretical results. The numerical simulations indicate that there is a good agreement between theoretical results and numerical ones.

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COVID-19 流行病分数阶数学模型的动力学。

在这项研究中，我们建立并分析了一个新的分数阶 COVID-19 流行病数学模型，该模型包含五个等级，即 S（易感等级）、E（暴露等级）、I（感染等级）、Q（隔离等级）。该模型由分数阶微分方程模型系统描述，包括五个等级，即 S（易感等级）、E（暴露等级）、I（感染等级）、Q（隔离等级）和 R（恢复等级）。对所提出的分数阶模型的动力学和数值近似进行了研究。首先，确定了模型的正定性和有界性。其次，利用下一代矩阵方法计算模型的基本繁殖数。然后，研究了模型的渐进稳定性。最后，我们应用自适应预测-校正算法和四阶 Runge-Kutta (RK4) 方法对提出的模型进行仿真。因此，我们进行了一系列数值模拟，以支持理论结果的正确性。数值模拟结果表明，理论结果与数值结果之间存在良好的一致性。

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来源期刊

Advances in Difference Equations 数学-数学

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0.00%

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审稿时长

4-8 weeks

期刊介绍： The theory of difference equations, the methods used, and their wide applications have advanced beyond their adolescent stage to occupy a central position in applicable analysis. In fact, in the last 15 years, the proliferation of the subject has been witnessed by hundreds of research articles, several monographs, many international conferences, and numerous special sessions. The theory of differential and difference equations forms two extreme representations of real world problems. For example, a simple population model when represented as a differential equation shows the good behavior of solutions whereas the corresponding discrete analogue shows the chaotic behavior. The actual behavior of the population is somewhere in between. The aim of Advances in Difference Equations is to report mainly the new developments in the field of difference equations, and their applications in all fields. We will also consider research articles emphasizing the qualitative behavior of solutions of ordinary, partial, delay, fractional, abstract, stochastic, fuzzy, and set-valued differential equations. Advances in Difference Equations will accept high-quality articles containing original research results and survey articles of exceptional merit.