Stochastic dynamics and probability analysis for a generalized epidemic model with environmental noise

Brahim Boukanjime and Mohamed Maama

Chaos, Solitons & Fractals, 2025, vol. 199, issue P2

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. We further establish V-geometric ergodicity, which guarantees the exponential convergence of the system’s probability distribution to its stationary measure, providing a quantitative measure of the system’s stability over time. By leveraging Young’s and Chebyshev’s inequalities, 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. Additionally, we derive conditions for stochastic extinction, which describes scenarios where the epidemic may eventually die out. Finally, we perform numerical simulations to verify our theoretical results and assess the model’s behavior under different parameters.

Keywords: Generalized epidemic model; Stochastically ultimate boundedness; Stochastic permanence; Stochastic extinction; V-geometric ergodicity (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S096007792500757X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:199:y:2025:i:p2:s096007792500757x

DOI: 10.1016/j.chaos.2025.116744

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().