A unified stochastic SIR model driven by Lévy noise with time-dependency
1Centre de recherche du CHU Sainte-Justine, Département de Mathématiques et de Statistique, Université de Montréal, Montreal, Canada.
Advances in Continuous and Discrete Models
|July 19, 2024
Summary
This study introduces a unified stochastic SIR model with Lévy noise, offering a flexible framework for disease dynamics. It establishes conditions for the model
Area of Science:
- Mathematical epidemiology
- Stochastic modeling
- Dynamical systems
Background:
- Traditional SIR models often assume simplified dynamics.
- Incorporating stochasticity and complex factors is crucial for realistic disease modeling.
Purpose of the Study:
- To develop a unified stochastic SIR model incorporating Lévy noise.
- To analyze the model's mathematical properties, including solution existence and uniqueness.
- To investigate disease extinction and persistence dynamics.
Main Methods:
- Development of a novel stochastic SIR model driven by Lévy noise.
- Mathematical analysis for existence and uniqueness of positive global solutions.
- Investigation of extinction and persistence criteria using stochastic methods.
Main Results:
- Established conditions for the existence and uniqueness of positive global solutions.
- Characterized the extinction and persistence behaviors of the disease.
- Demonstrated model applicability through examples and simulations.
Conclusions:
- The proposed unified stochastic SIR model provides a robust framework for analyzing complex disease dynamics.
- The model's flexibility allows for the inclusion of various real-world factors.
- Results offer insights into disease spread and control strategies.
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