A Unified Stochastic SIR Model Driven By L\'{e}vy Noise With Time-Dependency

TL;DR

This paper introduces a comprehensive stochastic SIR epidemic model incorporating Lévy noise, allowing for complex real-world factors like time-dependency and environmental disturbances, with theoretical analysis and simulations.

Contribution

It presents a new unified stochastic SIR model with Lévy noise that accounts for nonlinearity, discontinuity, and environmental effects, along with rigorous mathematical results.

Findings

Existence and uniqueness of positive global solutions

Conditions for extinction and persistence of the disease

Simulation results illustrating theoretical findings

Abstract

We propose a unified stochastic SIR model driven by L\'{e}vy noise. The model is structural enough to allow for time-dependency, nonlinearity, discontinuity, demography and environmental disturbances. We present concise results on the existence and uniqueness of positive global solutions and investigate the extinction and persistence of the novel model. Examples and simulations are provided to illustrate the main results.