Output trajectory controllability of a discrete-time sir epidemic model

Lahbib Benahmadi, Mustapha Lhous, Abdessamad Tridane, Mostafa Rachik

Research output: Contribution to journalArticlepeer-review


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 yd = (ydi)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.

Original languageEnglish
Article number16
JournalMathematical Modelling of Natural Phenomena
Publication statusPublished - 2023


  • Fixed point theorem
  • Optimal control
  • Output controllability
  • SIR-epidemic model
  • State-space technique

ASJC Scopus subject areas

  • Modelling and Simulation


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