Banerjee Ramashis, Biswas Raj Kumar
Department of Electrical Engineering, National Institute of Technology, Silchar, Pin-788010 India.
IFAC Pap OnLine. 2022;55(1):616-622. doi: 10.1016/j.ifacol.2022.04.101. Epub 2022 May 9.
In this work a compartmental SIR model has been proposed for describing the dynamics of COVID-19 with Caputo's fractional derivative(FD). SIR compartmental model has been used here with fractional differential equations(FDEs). The mathematical model of the pandemic consists of three compartments namely susceptible, infected and recovered individuals. The dynamics of the pandemic COVID-19 with FDEs for showing the effect of memory as most of the cell biological systems can be described accurately by FDEs Time dependent control(Effective vaccination) has been applied model to formulated fractional optimal control problem(FOCP) to reduce the viral load. Pontryagin's Maximum Principle(PMP) has been used to formulate FOCP. An effective vaccination is very helpful for controlling the pandemic, which is observed through the numerical simulation via Grunwald-Letnikov(G-L) approximation. All numerical simulation work has been carried in MATLAB platform.
在这项工作中，提出了一种 compartmental SIR 模型，用于用卡普托分数阶导数（FD）描述 COVID-19 的动态。这里使用了带有分数阶微分方程（FDEs）的 SIR compartmental 模型。该大流行病的数学模型由三个部分组成，即易感个体、感染个体和康复个体。由于大多数细胞生物系统可以用 FDEs 准确描述，因此用 FDEs 来展示记忆效应的 COVID-19 大流行病动态。已将时间相关控制（有效疫苗接种）应用于该模型，以制定分数阶最优控制问题（FOCP）来降低病毒载量。已使用庞特里亚金极大值原理（PMP）来制定 FOCP。通过基于 Grünwald-Letnikov（G-L）近似的数值模拟观察到，有效疫苗接种对控制大流行病非常有帮助。所有数值模拟工作均在 MATLAB 平台上进行。
