Fractional optimal control problem for an age-structured model of COVID-19 transmission

Abstract

\n 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 \n j\n the population is divided into seven classes namely susceptible \n \n \n S\n j\n \n ,\n \n exposed \n \n \n E\n j\n \n ,\n \n infected with high risk \n \n \n I\n \n h\n \n \n \n j\n \n \n ,\n \n infected with low risk \n \n \n I\n \n l\n \n \n \n j\n \n \n ,\n \n hospitalized \n \n \n H\n j\n \n ,\n \n recovered with and without psychological complications \n \n R\n \n 1\n \n j\n \n and \n \n \n R\n \n 2\n \n j\n \n ,\n \n 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 \n \n j\n ,\n \n 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.\n