A mathematical model of COVID-19 using fractional derivative: outbreak in India with dynamics of transmission and control.

IF 4.1 3区数学 Q1 Mathematics

Advances in Difference Equations Pub Date : 2020-01-01 Epub Date: 2020-07-22 DOI:10.1186/s13662-020-02834-3

Amjad Salim Shaikh, Iqbal Najiroddin Shaikh, Kottakkaran Sooppy Nisar

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引用次数: 143

Abstract

Since the first case of 2019 novel coronavirus disease (COVID-19) detected on 30 January, 2020, in India, the number of cases rapidly increased to 3819 cases including 106 deaths as of 5 April, 2020. Taking this into account, in the present work, we have analysed a Bats-Hosts-Reservoir-People transmission fractional-order COVID-19 model for simulating the potential transmission with the thought of individual response and control measures by the government. The real data available about number of infected cases from 14 March, 2000 to 26 March, 2020 is analysed and, accordingly, various parameters of the model are estimated or fitted. The Picard successive approximation technique and Banach's fixed point theory have been used for verification of the existence and stability criteria of the model. Further, we conduct stability analysis for both disease-free and endemic equilibrium states. On the basis of sensitivity analysis and dynamics of the threshold parameter, we estimate the effectiveness of preventive measures, predicting future outbreaks and potential control strategies of the disease using the proposed model. Numerical computations are carried out utilising the iterative Laplace transform method and comparative study of different fractional differential operators is done. The impacts of various biological parameters on transmission dynamics of COVID-19 is investigated. Finally, we illustrate the obtained results graphically.

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使用分数导数的COVID-19数学模型:传播和控制动态的印度疫情。

自2020年1月30日在印度发现首例2019年新型冠状病毒病(COVID-19)病例以来，截至2020年4月5日，病例数迅速增加至3819例，其中106例死亡。考虑到这一点，在本工作中，我们分析了一个蝙蝠-宿主-水库-人传播的分数阶COVID-19模型，以模拟个体响应和政府控制措施的潜在传播。对2000年3月14日至2020年3月26日感染病例数的现有实际数据进行了分析，并据此估计或拟合了模型的各种参数。利用Picard逐次逼近技术和Banach不动点理论验证了模型的存在性和稳定性判据。此外，我们对无病和地方性平衡状态进行了稳定性分析。在对阈值参数进行敏感性分析和动态分析的基础上，我们利用所提出的模型估计了预防措施的有效性，预测了疾病未来的爆发和潜在的控制策略。利用迭代拉普拉斯变换方法进行了数值计算，并对不同分数阶微分算子进行了比较研究。研究了各种生物学参数对新冠病毒传播动力学的影响。最后，用图形说明了所得结果。

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来源期刊

Advances in Difference Equations 数学-数学

自引率

0.00%

发文量

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.