Denu Dawit, Kermausuor Seth
Department of Mathematical Sciences, Georgia Southern University, Savannah, GA 31419, USA.
Department of Mathematics and Computer Science, Alabama State University, Montgomery, AL 36101, USA.
Vaccines (Basel). 2022 Oct 22;10(11):1773. doi: 10.3390/vaccines10111773.
The outbreak of the coronavirus disease (COVID-19) has caused a lot of disruptions around the world. In an attempt to control the spread of the disease among the population, several measures such as lockdown, and mask mandates, amongst others, were implemented by many governments in their countries. To understand the effectiveness of these measures in controlling the disease, several mathematical models have been proposed in the literature. In this paper, we study a mathematical model of the coronavirus disease with lockdown by employing the Caputo fractional-order derivative. We establish the existence and uniqueness of the solution to the model. We also study the local and global stability of the disease-free equilibrium and endemic equilibrium solutions. By using the residual power series method, we obtain a fractional power series approximation of the analytic solution. Finally, to show the accuracy of the theoretical results, we provide some numerical and graphical results.
冠状病毒病（COVID-19）的爆发在全球造成了诸多混乱。为控制疾病在人群中的传播，许多国家的政府实施了诸如封锁和强制戴口罩等多项措施。为了解这些措施在控制疾病方面的有效性，文献中提出了几种数学模型。在本文中，我们通过使用卡普托分数阶导数研究一个带有封锁措施的冠状病毒病数学模型。我们建立了该模型解的存在性和唯一性。我们还研究了无病平衡点和地方病平衡点解的局部和全局稳定性。通过使用残差幂级数方法，我们得到了解析解的分数幂级数近似。最后，为了展示理论结果的准确性，我们给出了一些数值和图形结果。
