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Fractional dynamic analysis and optimal control problem for an SEIQR model on complex networks.

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  • 1School of Mathematical and Statistics, Guizhou University, Guiyang 550025, Guizhou, China.

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Summary

This study introduces a fractional order susceptible-exposed-infected-quarantined-recovered model on complex networks. It analyzes parameter influence on the basic reproduction number (R0) and applies optimal control strategies for disease management.

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Network Science

Background:

  • Complex networks are crucial for understanding disease transmission dynamics.
  • Fractional order models offer a more nuanced approach to compartmental disease modeling.

Purpose of the Study:

  • To establish and analyze a fractional order susceptible-exposed-infected-quarantined-recovered (SEIQR) model on complex networks.
  • To determine the basic reproduction number (R0) and assess model stability.
  • To investigate optimal control strategies for disease mitigation.

Main Methods:

  • Development of a fractional order SEIQR model.
  • Calculation of the basic reproduction number (R0).
  • Proof of existence, uniqueness, and Ulam-Hyers stability.
  • Latin hypercube sampling-partial rank correlation coefficient (LHS-PRCC) for parameter sensitivity analysis.
  • Pontryagin's minimum principle for optimal control.
  • Prediction correction method for numerical simulations.

Main Results:

  • A specific expression for R0 was derived.
  • The existence, uniqueness, and Ulam-Hyers stability of the model solution were proven.
  • Parameter influence on R0 was quantified using LHS-PRCC.
  • Optimal vaccination and quarantine rates were determined using Pontryagin's minimum principle.
  • Simulations showed the effects of fractional order (α), node degree, and network size on disease dynamics.

Conclusions:

  • The fractional order SEIQR model provides a robust framework for studying infectious diseases on complex networks.
  • Parameter analysis and optimal control strategies are essential for effective disease management.
  • Fractional calculus and network structure significantly impact disease transmission patterns.