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Numerical dynamics and optimal control for multi-strain age-structured epidemic model.

Zhijie Chen1, Hanmeng Feng2

  • 1College of Mathematical Sciences, Harbin Engineering University, Harbin, China. chenzhijie0711@hrbeu.edu.cn.

Journal of Mathematical Biology
|January 17, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a new age-structured epidemiological model for multiple viral strains. It presents a numerical framework for analyzing disease dynamics and optimal control, ensuring biological meaning is preserved.

Keywords:
Basic reproduction numberDynamicsLinearly implicit Euler methodMulti-strain SIR modelsOptimal control

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Computational Science

Background:

  • Understanding the spread of infectious diseases requires sophisticated models.
  • Multi-strain models are crucial for capturing complex epidemic dynamics.
  • Age structure significantly impacts disease transmission patterns.

Purpose of the Study:

  • To propose a novel age-structured epidemiological model incorporating multiple viral strains.
  • To develop a robust numerical framework for analyzing the dynamics and optimal control of such models.
  • To provide a unified approach for studying long-time behavior in multi-strain epidemic models.

Main Methods:

  • Development of a linearly implicit Euler method for numerical simulations.
  • Derivation of first-order convergence based on uniform numerical boundedness.
  • Analysis of numerical dynamics using a numerical basic reproduction number.

Main Results:

  • The numerical framework preserves biological meaning unconditionally.
  • Numerical dynamics are governed by a numerical basic reproduction number, indicating equilibrium stability.
  • The framework is verified through numerical simulations for an age-structured SIR model.

Conclusions:

  • The proposed framework offers an effective and unified approach for multi-strain epidemic models.
  • It provides a numerical optimal control strategy for age-structured SIR models.
  • The method demonstrates efficiency and accuracy in simulating complex epidemic scenarios.