Stochastic Dynamics and Probability Analysis for a Generalized Epidemic Model with Environmental Noise

TL;DR

This paper analyzes a stochastic epidemic model with environmental noise, establishing conditions for long-term behavior, extinction, and convergence, supported by theoretical proofs and numerical simulations.

Contribution

It introduces a generalized stochastic SEIQR model with new analytical results on stability, extinction, and ergodicity under environmental noise.

Findings

Proves existence and uniqueness of global positive solutions.

Derives conditions for stochastic extinction and ergodicity.

Numerical simulations confirm theoretical predictions.

Abstract

In this paper we consider a stochastic SEIQR (susceptible-exposed-infected-quarantined-recovered) epidemic model with a generalized incidence function. Using the Lyapunov method, we establish the existence and uniqueness of a global positive solution to the model, ensuring that it remains well-defined over time. Through the application of Young's inequality and Chebyshev's inequality, we demonstrate the concepts of stochastic ultimate boundedness and stochastic permanence, providing insights into the long-term behavior of the epidemic dynamics under random perturbations. Furthermore, we derive conditions for stochastic extinction, which describe scenarios where the epidemic may eventually die out, and V-geometric ergodicity, which indicates the rate at which the system's state converges to its equilibrium. Finally, we perform numerical simulations to verify our theoretical results and assess the model's behavior under different parameters.