Output trajectory controllability of a discrete-time sir epidemic model

¹ Fundamental and Applied Mathematics Laboratory, Department of Mathematics and Computer Science, Faculty of Sciences Ain Chock, Hassan II University of Casablanca, B.P. 5366 Maarif Casablanca, Morocco
² Department of Mathematical Sciences, United Arab Emirates University, Al-Ain PO Box 15551, UAE
³ Laboratory of Analysis Modelling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University of Casablanca, Sidi Othman Casablanca B.P. 7955, Morocco

^* Corresponding author: a-tridane@uaeu.ac.ae

Received: 7 October 2022
Accepted: 20 April 2023

Abstract

Developing new approaches that help control the spread of infectious diseases is a critical issue for public health. Such approaches must consider the available resources and capacity of the healthcare system. In this paper, we present a new mathematical approach to controlling an epidemic model by investigating the optimal control that aims to bring the output of the epidemic to target a desired disease output y^d = (y^d_i)_{i∈{0,...,N}}. First, we use the state-space technique to transfer the trajectory controllability to optimal control with constraints on the final state. Then, we use the fixed point theorems to determine the set of admissible controls and solve the output trajectory controllability problem. Finally, we apply our method to the model of a measles epidemic, and we give a numerical simulation to illustrate the findings of our approach.