A mathematical model of Coronavirus Disease (COVID-19) containing asymptomatic and symptomatic classes.
A mathematical model of Coronavirus Disease (COVID-19) containing asymptomatic and symptomatic classes.
复制标题
冠状病毒疾病（COVID-19）的数学模型，包含无症状和有症状的类别。
DOI：
10.1016/j.rinp.2020.103776
复制
发表时间：
2021-03
影响因子：
5.3
通讯作者：
Yusuf I
中科院分区：
文献类型：
--
作者：
Ahmed I;Modu GU;Yusuf A;Kumam P;Yusuf I
本文的研究工作试图利用常微分方程和分数阶微分方程建立数学模型来描述2019冠状病毒病（COVID-19）的爆发。一段时间以来，这种疾病在全球范围内的传播一直在加剧，而且看不到尽头。该研究使用尼日利亚COVID-19病例数据进行数值模拟，并将其拟合到该模型中。我们考虑了无症状感染者和有症状感染者，暴露者要么先被隔离，要么转移到感染班级，易感个体也有可能直接转移到隔离班级。结果表明，该模型具有两个平衡点；无病平衡点和地方病平衡点。平衡点的稳定性分析表明，当基本复制数为0时，平衡点是局部渐近稳定的，当基本复制数为0时，平衡点是全局渐近稳定的。对这些参数进行了敏感性分析，并利用显示疾病传播的参数的拟合值描绘了每个状态变量的轮廓。最敏感的参数是易感个体之间的接触率和个体从暴露类向有症状感染类转移的率。此外，数据的基本复制数计算为。利用不动点定理建立了解的存在唯一性。利用最小二乘曲线拟合方法，结合MATLAB优化工具箱中的fminsearch函数，对模型中涉及的一些未知生物参数求出了最优值。此外，我们使用Atangana-Toufik数值格式对分数模型进行了数值求解，并给出了不同形式的图形结果，可用于最小化感染。
The research work in this paper attempts to describe the outbreak of Coronavirus Disease 2019 (COVID-19) with the help of a mathematical model using both the Ordinary Differential Equation (ODE) and Fractional Differential Equation. The spread of the disease has been on the increase across the globe for some time with no end in sight. The research used the data of COVID-19 cases in Nigeria for the numerical simulation which has been fitted to the model. We brought in the consideration of both asymptomatic and symptomatic infected individuals with the fact that an exposed individual is either sent to quarantine first or move to one of the infected classes with the possibility that susceptible individual can also move to quarantined class directly. It was found that the proposed model has two equilibrium points; the disease-free equilibrium point and the endemic equilibrium point . Stability analysis of the equilibrium points shows is locally asymptotically stable whenever the basic reproduction number, and is globally asymptotically stable whenever . Sensitivity analysis of the parameters in the was conducted and the profile of each state variable was also depicted using the fitted values of the parameters showing the spread of the disease. The most sensitive parameters in the are the contact rate between susceptible individuals and the rate of transfer of individuals from exposed class to symptomatically infected class. Moreover, the basic reproduction number for the data is calculated as . Existence and uniqueness of solution established via the technique of fixed point theorem. Also, using the least square curve fitting method together with the fminsearch function in the MATLAB optimization toolbox, we obtain the best values for some of the unknown biological parameters involved in the proposed model. Furthermore, we solved the fractional model numerically using the Atangana-Toufik numerical scheme and presenting different forms of graphical results that can be useful in minimizing the infection.
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