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Finite-time analysis of epidemic reaction-diffusion models: Stability, synchronization, and numerical insights.

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Summary

This study introduces a new method for analyzing finite-time stability and synchronization in reaction-diffusion systems, crucial for epidemiological modeling. The approach enhances understanding of transient dynamics in spatially extended systems.

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Area of Science:

  • Applied Mathematics
  • Control Theory
  • Epidemiological Modeling

Background:

  • Reaction-diffusion systems are vital for modeling spatially extended phenomena.
  • Analyzing finite-time stability and synchronization in these systems remains a challenge.
  • Epidemiological models often involve complex, nonlinear, and spatially distributed dynamics.

Purpose of the Study:

  • To develop a novel framework for analyzing finite-time stability (FTS) and finite-time synchronization (FTSYN) in integer-order reaction-diffusion systems.
  • To investigate the transient dynamics of spatially extended systems within finite time frames.
  • To apply these analytical tools to epidemiological modeling.

Main Methods:

  • Integration of Gronwall's inequality.
  • Utilization of Lyapunov functionals (LFs).
  • Application of linear control strategies.

Main Results:

  • A comprehensive framework for analyzing FTS and FTSYN in reaction-diffusion systems was established.
  • Theoretical advancements were made in understanding the transient dynamics of spatially extended systems.
  • MATLAB simulations confirmed the effectiveness of the proposed control schemes.

Conclusions:

  • The developed methodology provides robust tools for analyzing and managing nonlinear systems with rapid convergence requirements.
  • The findings offer significant implications for epidemiological modeling, particularly in understanding disease transmission dynamics.
  • This work bridges theoretical analysis with practical applications in complex systems.