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

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.