A Novel Stochastic SVIR Model Capturing Transmission Variability Through Mean-Reverting Processes and Stationary Reproduction Thresholds

Yassine Sabbar () and Saud Fahad Aldosary ()
Additional contact information
Yassine Sabbar: IMIA Laboratory, T-IDMS, Department of Mathematics, FST Errachidia, Moulay Ismail University of Meknes, P.O. Box 509, Errachidia 52000, Morocco
Saud Fahad Aldosary: Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia

Mathematics, 2025, vol. 13, issue 13, 1-24

Abstract: This study presents a stochastic SVIR epidemic model in which disease transmission rates fluctuate randomly over time, driven by independent, mean-reverting processes with multiplicative noise. These dynamics capture environmental variability and behavioral changes affecting disease spread. We derive analytical expressions for the conditional moments of the transmission rates and establish the existence of their stationary distributions under broad conditions. By averaging over these distributions, we define a stationary effective reproduction number that enables a probabilistic classification of outbreak scenarios. Specifically, we estimate the likelihood of disease persistence or extinction based on transmission uncertainty. Sensitivity analyses reveal that the shape and intensity of transmission variability play a decisive role in epidemic outcomes. Monte Carlo simulations validate our theoretical findings, showing strong agreement between empirical distributions and theoretical predictions. Our results underscore how randomness in disease transmission can fundamentally alter epidemic trajectories, offering a robust mathematical framework for risk assessment under uncertainty.

Keywords: stochastic epidemic models; inverse gamma distribution; effective reproduction number; ergodic transmission rates (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/13/2097/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/13/2097/ (text/html)

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:gam:jmathe:v:13:y:2025:i:13:p:2097-:d:1687817

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().