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 $(\mathit{DFE})$ and the endemic equilibrium point $(E_1)$. Stability analysis of the equilibrium points shows $(E_0)$ is locally asymptotically stable whenever the basic reproduction number, ${\mathcal{R}}_0<1$ and $(E_1)$ is globally asymptotically stable whenever ${\mathcal{R}}_0>1$. Sensitivity analysis of the parameters in the ${\mathcal{R}}_0$ 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 ${\mathcal{R}}_0$ 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 ${\mathcal{R}}_0\approx 1.7031$. 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.

本文的研究工作试图借助使用常微分方程 (ODE) 和分数阶微分方程的数学模型来描述 2019 年冠状病毒病 (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，而且还没有结束的迹象。该研究使用尼日利亚的COVID-19病例数据进行数值模拟，并将其拟合到模型中。我们考虑了无症状和有症状的感染者，因为暴露者要么首先被送去隔离，要么转移到感染班级之一，易感者也可能直接转移到隔离班级。发现所提出的模型有两个平衡点；无病平衡点$（\mathit{分布式FE}）$和地方病平衡点$（{乙}_1）$。平衡点的稳定性分析表明$（{乙}_0）$每当基本再生数时，局部渐近稳定，${\mathcal{右}}_0<1$和$（{乙}_1）$是全局渐近稳定的，只要${\mathcal{右}}_0>1$。中参数的敏感性分析${\mathcal{右}}_0$进行了研究，并使用显示疾病传播的参数的拟合值描述了每个状态变量的概况。最敏感的参数${\mathcal{右}}_0$是易感个体之间的接触率以及个体从暴露类别转移到有症状感染类别的比率。此外，数据的基本再生数计算为${\mathcal{右}}_0\approx 1.7031$。通过不动点定理技术建立解的存在性和唯一性。此外，使用最小二乘曲线拟合方法以及MATLAB优化工具箱中的fminsearch函数，我们获得了所提出模型中涉及的一些未知生物参数的最佳值。此外，我们使用 Atangana-Toufik 数值方案对分数模型进行了数值求解，并呈现了不同形式的图形结果，这些结果可用于最大限度地减少感染。