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<p>We formulate an epidemic mathematical model with multiple delays to explore the dynamics of the disease. First, we introduce the SIR model that incorporates vaccination and quarantine components in conjunction with consideration of multiple time delays. Additionally, Hopf bifurcation appears when the delay reaches a&#xa0;critical value, as demonstrated in our stability analysis, especially when two-time delays are simultaneously considered bifurcation parameters, producing oscillatory dynamics. The local stability of the endemic and disease-free equilibrium points (DFE) is studied in detail for all possible delay configurations. We also perform a&#xa0;sensitivity analysis of the basic reproduction number (BRN) concerning various model parameters. As part of the control measures, the effect of public awareness through educational campaigns is taken into account. An optimal control framework is then developed to minimize disease spread and control expenses, and the corresponding control approach is elaborated. The resolution of this optimization problem is presented, accompanied by numerical simulations to illustrate the analytical findings.</p>

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Dynamic properties and computational studies for a nonlinear multi-delay epidemic model

  • 期刊论文

  • 发表日期：

    2025年1月1日

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  • H. Ismail,
  • S. Hariharan,
  • L. Shangerganesh,
  • A. Debbouche,
  • S. V. Kashtanova

摘要

We formulate an epidemic mathematical model with multiple delays to explore the dynamics of the disease. First, we introduce the SIR model that incorporates vaccination and quarantine components in conjunction with consideration of multiple time delays. Additionally, Hopf bifurcation appears when the delay reaches a critical value, as demonstrated in our stability analysis, especially when two-time delays are simultaneously considered bifurcation parameters, producing oscillatory dynamics. The local stability of the endemic and disease-free equilibrium points (DFE) is studied in detail for all possible delay configurations. We also perform a sensitivity analysis of the basic reproduction number (BRN) concerning various model parameters. As part of the control measures, the effect of public awareness through educational campaigns is taken into account. An optimal control framework is then developed to minimize disease spread and control expenses, and the corresponding control approach is elaborated. The resolution of this optimization problem is presented, accompanied by numerical simulations to illustrate the analytical findings.