Khajji Bouchaib, Kouidere Abdelfatah, Elhia Mohamed, Balatif Omar, Rachik Mostafa
Laboratory of Analysis Modelling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M'Sik, Hassan II University, Sidi Othman, Casablanca, Morocco.
MAEGE Laboratory, FSJES Ain Sebaa, Hassan II University, Casablanca, Morocco.
Chaos Solitons Fractals. 2021 Feb;143:110625. doi: 10.1016/j.chaos.2020.110625. Epub 2021 Jan 2.
The aim of this study is to model the transmission of COVID-19 and investigate the impact of some control strategies on its spread. We propose an extension of the classical SEIR model, which takes into account the age structure and uses fractional-order derivatives to have a more realistic model. For each age group the population is divided into seven classes namely susceptible exposed infected with high risk infected with low risk hospitalized recovered with and without psychological complications and respectively. In our model, we incorporate three control variables which represent: awareness campaigns, diagnosis and psychological follow-up. The purpose of our control strategies is protecting susceptible individuals from being infected, minimizing the number of infected individuals with high and low risk within a given age group as well as reducing the number of recovered individuals with psychological complications. Pontryagin's maximum principle is used to characterize the optimal controls and the optimality system is solved by an iterative method. Numerical simulations performed using Matlab, are provided to show the effectiveness of three control strategies and the effect of the order of fractional derivative on the efficiency of these control strategies. Using a cost-effectiveness analysis method, our results show that combining awareness with diagnosis is the most effective strategy. To the best of our knowledge, this work is the first that propose a framework on the control of COVID-19 transmission based on a multi-age model with Caputo time-fractional derivative.
本研究的目的是对新冠病毒（COVID-19）的传播进行建模，并研究一些控制策略对其传播的影响。我们提出了经典SEIR模型的一种扩展，该扩展考虑了年龄结构，并使用分数阶导数以获得更现实的模型。对于每个年龄组，人群被分为七个类别，即易感者、暴露者、高风险感染者、低风险感染者、住院者、有和没有心理并发症的康复者。在我们的模型中，我们纳入了三个控制变量，分别代表：宣传活动、诊断和心理随访。我们控制策略的目的是保护易感个体不被感染，在给定年龄组内将高风险和低风险感染者的数量降至最低，以及减少有心理并发症的康复者数量。庞特里亚金极大值原理用于刻画最优控制，最优性系统通过迭代方法求解。使用Matlab进行的数值模拟表明了三种控制策略的有效性以及分数阶导数的阶数对这些控制策略效率的影响。使用成本效益分析方法，我们的结果表明将宣传与诊断相结合是最有效的策略。据我们所知，这项工作是首次基于具有卡普托时间分数阶导数的多年龄模型提出新冠病毒传播控制框架。
