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Stochastic delayed analysis of coronavirus model through efficient computational method.

Naveed Shahid1, Ali Raza2, Sana Iqbal1

  • 1Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan.

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Summary
This summary is machine-generated.

This study introduces a new stochastic delayed model for infectious disease dynamics, offering realistic insights into disease control. The model accurately predicts disease extinction or persistence, crucial for managing outbreaks like COVID-19.

Keywords:
Computational methodsCovid-19 disease modelExistence and uniquenessLyapunov functionReproduction numberStability resultsStochastic delayed differential equations (SDDEs)

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Computational Science

Background:

  • Stochastic delayed modeling provides realistic insights into infectious disease transmission dynamics.
  • COVID-19, despite global control efforts, persists through variants, necessitating advanced modeling approaches.
  • Existing models often struggle with the complexity of real-world disease spread.

Purpose of the Study:

  • To develop and analyze a novel stochastic delayed mathematical model for infectious diseases.
  • To investigate the dynamics of disease transmission, including extinction and persistence.
  • To assess the efficacy of numerical methods for solving complex stochastic delayed differential equations.

Main Methods:

  • Construction of a stochastic delayed model using nonlinear stochastic delayed differential equations (SDDEs).
  • Application of transition probabilities and parametric perturbation methods.
  • Analysis of fundamental properties: positivity, boundedness, existence, uniqueness, and stability of equilibria.
  • Utilizing established theorems to study disease extinction and persistence.
  • Implementation and comparison of numerical methods, including nonstandard finite difference schemes.

Main Results:

  • The proposed stochastic delayed model accurately captures disease dynamics.
  • Analysis confirmed the model's fundamental properties and stability of equilibria.
  • The study provides conditions for disease extinction and persistence.
  • The nonstandard finite difference method demonstrated effectiveness in preserving model properties.

Conclusions:

  • The developed stochastic delayed model offers a robust framework for understanding infectious disease control.
  • The proposed numerical method ensures accurate simulation of disease dynamics.
  • This research contributes to improved strategies for managing and mitigating infectious disease threats.