论文标题
使用分数衍生物具有潜在健康状况的COVID-19的数学模型
A mathematical model of COVID-19 with an underlying health condition using fraction order derivative
论文作者
论文摘要
研究表明，有些患有癌症，心力衰竭，糖尿病和高血压等潜在疾病的人更有可能获得covid-19，并且结果较差。在本文中，提出了一个分数衍生物，以研究Covid-19的传播动力学，考虑到具有潜在条件的人群。分数衍生物是在Atangana Beleanu和Caputo（ABC）的意义中定义的。对于提出的模型，我们找到基本的生殖数，平衡点并确定这些平衡点的稳定性。解决方案的存在和独特性与Hyers Ulam稳定性一起建立。进行了操作员的数值方案以获得数值模拟以支持分析结果。从加纳3月至2020年6月的Covid-19案件被用来验证该模型。数值模拟显示，随着分数操作员在120天内的0.6增加，感染的下降。时间依赖性最佳控制已纳入模型。最佳控制的数值模拟显示，疫苗接种减少了容易受到COVID-19的个体的数量，暴露于COVID-19和Covid-19和Covid-19患者，患有和没有潜在的健康状况的患者。
Studies have shown that some people with underlying conditions such as cancer, heart failure, diabetes and hypertension are more likely to get COVID-19 and have worse outcomes. In this paper, a fractional-order derivative is proposed to study the transmission dynamics of COVID-19 taking into consideration population having an underlying condition. The fractional derivative is defined in the Atangana Beleanu and Caputo (ABC) sense. For the proposed model, we find the basic reproductive number, the equilibrium points and determine the stability of these equilibrium points. The existence and the uniqueness of the solution are established along with Hyers Ulam Stability. The numerical scheme for the operator was carried out to obtain a numerical simulation to support the analytical results. COVID-19 cases from March to June 2020 of Ghana were used to validate the model. The numerical simulation revealed a decline in infections as the fractional operator was increased from 0.6 within the 120 days. Time-dependent optimal control was incorporated into the model. The numerical simulation of the optimal control revealed, vaccination reduces the number of individuals susceptible to the COVID-19, exposed to the COVID-19 and Covid-19 patients with and without an underlying health condition.
