A fractional order mathematical model for COVID-19 dynamics with quarantine, isolation, and environmental viral load.

IF 4.1 3区 数学 Q1 Mathematics
Advances in Difference Equations Pub Date : 2021-01-01 Epub Date: 2021-02-11 DOI:10.1186/s13662-021-03265-4
Mohammed A Aba Oud, Aatif Ali, Hussam Alrabaiah, Saif Ullah, Muhammad Altaf Khan, Saeed Islam
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引用次数: 101

Abstract

COVID-19 or coronavirus is a newly emerged infectious disease that started in Wuhan, China, in December 2019 and spread worldwide very quickly. Although the recovery rate is greater than the death rate, the COVID-19 infection is becoming very harmful for the human community and causing financial loses to their economy. No proper vaccine for this infection has been introduced in the market in order to treat the infected people. Various approaches have been implemented recently to study the dynamics of this novel infection. Mathematical models are one of the effective tools in this regard to understand the transmission patterns of COVID-19. In the present paper, we formulate a fractional epidemic model in the Caputo sense with the consideration of quarantine, isolation, and environmental impacts to examine the dynamics of the COVID-19 outbreak. The fractional models are quite useful for understanding better the disease epidemics as well as capture the memory and nonlocality effects. First, we construct the model in ordinary differential equations and further consider the Caputo operator to formulate its fractional derivative. We present some of the necessary mathematical analysis for the fractional model. Furthermore, the model is fitted to the reported cases in Pakistan, one of the epicenters of COVID-19 in Asia. The estimated value of the important threshold parameter of the model, known as the basic reproduction number, is evaluated theoretically and numerically. Based on the real fitted parameters, we obtained R 0 1.50 . Finally, an efficient numerical scheme of Adams-Moulton type is used in order to simulate the fractional model. The impact of some of the key model parameters on the disease dynamics and its elimination are shown graphically for various values of noninteger order of the Caputo derivative. We conclude that the use of fractional epidemic model provides a better understanding and biologically more insights about the disease dynamics.

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具有隔离、隔离和环境病毒载量的COVID-19动态的分数阶数学模型
COVID-19或冠状病毒是一种新出现的传染病,于2019年12月在中国武汉开始,并迅速在全球传播。虽然康复率大于死亡率,但新冠病毒感染对人类社会的危害非常大,给经济造成了经济损失。市场上还没有针对这种感染的适当疫苗来治疗感染者。最近已经实施了各种方法来研究这种新型感染的动力学。在这方面,数学模型是了解COVID-19传播模式的有效工具之一。在本文中,我们建立了一个考虑检疫、隔离和环境影响的卡普托意义上的分数流行病模型,以检验COVID-19爆发的动态。分数模型对于更好地理解疾病流行以及捕捉记忆和非局域效应非常有用。首先,我们在常微分方程中构造模型,并进一步考虑Caputo算子来表示其分数阶导数。我们给出了分数阶模型的一些必要的数学分析。此外,该模型适用于巴基斯坦报告的病例,巴基斯坦是亚洲COVID-19的中心之一。对模型的重要阈值参数即基本再现数的估计值进行了理论和数值计算。根据实际拟合参数,得到R 0≈1.50。最后,采用Adams-Moulton型数值格式对分数阶模型进行了数值模拟。对于卡普托导数的不同非整数阶值,用图形显示了一些关键模型参数对疾病动力学及其消除的影响。我们的结论是,使用分数流行病模型提供了更好的理解和生物学上更多的关于疾病动力学的见解。
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来源期刊
自引率
0.00%
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0
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.
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