A MATHEMATICAL MODELING OF COVID-19 WITH OPTIMAL CONTROL DYNAMICS: INSIGHTS FROM IRAN

Articles in Press

Document Type : Research Paper

Authors

1 Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.

2 Department of Mathematics, Faculty of Science, University of Zabol, Zabol, Iran.

Abstract

In this paper, we propose a mathematical model for the transmission of
coronavirus-19 disease (COVID-19) to understand under which conditions it will be
eradicated or persisted. The dynamics of COVID-19 for this study is divided into
seven classes: susceptible, vaccinated, exposed, symptomatically infected, a symptomatically infected, quarantined, and recovered. The model has both disease-free
and endemic equilibria. The basic reproduction number (R0) is computed using the
next-generation matrix method. It is shown that the disease-free equilibrium is both
locally and globally asymptotically stable, whereas the endemic equilibrium is proved
to be only locally asymptotically stable. From March 31, 2020, to July 31, 2021, Iran
experienced four waves of COVID-19. The observed monthly cumulative cases were
approximated by quadratic polynomials, and their shapes were evaluated for consistency with the qualitative dynamics predicted by the model. We have formulated
and solved an optimal control problem to understand the effects of performance of
vaccination of susceptible individuals and treatment of quarantined individuals to
hinder the outbreak of this illness. Finally, sensitivity analysis and numerical simulations confirmed that the implementation of quarantine, vaccination, and putting
on face masks will help to minimize the spread of the COVID-19 virus.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 01 July 2026

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History

  • Receive Date: 02 November 2025
  • Revise Date: 20 May 2026
  • Accept Date: 01 July 2026

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