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Peer-reviewedCC BY 4.0Infectious Disease Modelling

A Comparative Optimal Control Study of Protecting Susceptibles and Isolating Infecteds in SIR Models

  • Mohammed Elghandouri1
  • Mostafa Adimy1
  • Claudia Pio Ferreira2
  1. 1Inria, CNRS, Centrale Lyon, INSA Lyon, Universite Claude Bernard Lyon 1, Université Jean Monnet, ICJ UMR5208, Villeurbanne, 69603, France.
  2. 2São Paulo State University (UNESP), Institute of Biosciences, Botucatu, São Paulo, 18618-689, Brazil.
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Abstract

There are several approaches to controlling the spread of infectious diseases. Among the most widely used measures are the protection of susceptible individuals and the isolation of infected ones. This raises a critical question: which strategy, protecting susceptible individuals, isolating infected ones, or combining both, most effectively mitigates disease transmission? The work proposed here, address this question by analyzing protection and isolation strategies within the framework of the classical SIR (Susceptible-Infected-Recovered) epidemic model. Three scenarios are considered: (i) combined protection and isolation, (ii) protection alone, and (iii) isolation alone. Using Optimal Control Theory, we show that, in the short-term context of epidemic control, combining protection and isolation generally provides the most effective strategy under the considered conditions. However, when the combination is unavailable or unnecessary, isolation tends to outperform protection, particularly under challenging conditions such as high transmission rates or low recovery rates. Protection alone can still be effective, but primarily in settings where recovery rates are sufficiently high. These results contrast with those obtained from autonomous models, in which, in the long-term dynamics, protecting susceptible individuals proved to be more effective than isolating the infected.

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Cite

BibTeXRIS
BibTeX
@article{elghandouri2026comparative,
  title = {{A Comparative Optimal Control Study of Protecting Susceptibles and Isolating Infecteds in SIR Models}},
  author = {Mohammed Elghandouri and Mostafa Adimy and Claudia Pio Ferreira},
  journal = {Infectious Disease Modelling},
  year = {2026},
  month = sep,
  doi = {10.1016/j.idm.2026.08.002},
  url = {https://hal.science/hal-05521812v3},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - A Comparative Optimal Control Study of Protecting Susceptibles and Isolating Infecteds in SIR Models
AU  - Mohammed Elghandouri
AU  - Mostafa Adimy
AU  - Claudia Pio Ferreira
PY  - 2026
DA  - 2026/09/07
JO  - Infectious Disease Modelling
DO  - 10.1016/j.idm.2026.08.002
UR  - https://hal.science/hal-05521812v3
AB  - There are several approaches to controlling the spread of infectious diseases. Among the most widely used measures are the protection of susceptible individuals and the isolation of infected ones. This raises a critical question: which strategy, protecting susceptible individuals, isolating infected ones, or combining both, most effectively mitigates disease transmission? The work proposed here, address this question by analyzing protection and isolation strategies within the framework of the classical SIR (Susceptible-Infected-Recovered) epidemic model. Three scenarios are considered: (i) combined protection and isolation, (ii) protection alone, and (iii) isolation alone. Using Optimal Control Theory, we show that, in the short-term context of epidemic control, combining protection and isolation generally provides the most effective strategy under the considered conditions. However, when the combination is unavailable or unnecessary, isolation tends to outperform protection, particularly under challenging conditions such as high transmission rates or low recovery rates. Protection alone can still be effective, but primarily in settings where recovery rates are sufficiently high. These results contrast with those obtained from autonomous models, in which, in the long-term dynamics, protecting susceptible individuals proved to be more effective than isolating the infected.
SN  - 2468-0427
SN  - 2468-2152
ER  -