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<p>Human psychological responses play an important role in the spread of epidemics, and considering the psychological behavior factor as part of the spread of diseases can remarkably improve control efforts. Here, we introduce two optimal control strategies of a Susceptible-Infected-Recovered (SIR) model incorporating a non-linear incident rate describing the <i>psychological effects</i> of the population. The first strategy is without constraint and the other one is with a budget constraint in terms of an integral cost. The optimal strategy consists in minimizes the maximum number of infected individuals, that is by maintaining the infectious agent at a specific value until the corresponding <i>collective immunity threshold</i> is acquired. We supply the study with practical recommendations for policymakers and numerical simulations for further understanding and discussion.</p>

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Optimal control of a Susceptible-Infected-Recovered model with Capasso–Serio incident rate

  • 期刊论文

  • 发表日期：

    2026年3月9日

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  • Soufiane Boumasmoud,
  • Khalil Ezzinbi,
  • Aboudramane Guiro

摘要

Human psychological responses play an important role in the spread of epidemics, and considering the psychological behavior factor as part of the spread of diseases can remarkably improve control efforts. Here, we introduce two optimal control strategies of a Susceptible-Infected-Recovered (SIR) model incorporating a non-linear incident rate describing the psychological effects of the population. The first strategy is without constraint and the other one is with a budget constraint in terms of an integral cost. The optimal strategy consists in minimizes the maximum number of infected individuals, that is by maintaining the infectious agent at a specific value until the corresponding collective immunity threshold is acquired. We supply the study with practical recommendations for policymakers and numerical simulations for further understanding and discussion.