On the stochastic modeling and forecasting of the $ \mathscr{SVIR} $ epidemic dynamic model under environmental white noise

Shah Hussain; Naveed Iqbal; Elissa Nadia Madi; Mohsen Bakouri; Ilyas Khan; Wei Sin Koh; Shah Hussain; Naveed Iqbal; Elissa Nadia Madi; Mohsen Bakouri; Ilyas Khan; Wei Sin Koh

doi:10.3934/math.2025186

AIMS Mathematics

2025, Volume 10, Issue 2: 3983-3999. doi: 10.3934/math.2025186

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Research article

On the stochastic modeling and forecasting of the $ \mathscr{SVIR} $ epidemic dynamic model under environmental white noise

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
2.
Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin (UniSZA), Besut Campus, Terengganu, Malaysia
3.
Department of Medical Equipment Technology, College of Applied Medical Science, Majmaah University, Al Majmaah 11952, Saudi Arabia
4.
Department of Physics, College of Arts, Fezzan University, Traghen 71340, Libya
5.
Department of Mathematics, College of Science, Al-Zulfi, Majmaah University, Al Majmaah 11952, Saudi Arabia
6.
Hourani Center for Applied Scientific Research, Al-Ahliyya Amman University, Amman, Jordan
7.
INTI International University, Persiaran Perdana BBN Putra Nilai, 71800 Nilai, Negeri Sembilan, Malaysia

Received: 04 January 2025 Revised: 03 February 2025 Accepted: 11 February 2025 Published: 27 February 2025
MSC : 26A33, 34A08, 35R11

This study introduced a novel $ \mathscr{SVIR} $ epidemic model incorporating environmental white noise to account for stochastic fluctuations in disease transmission. The model was analyzed to determine conditions for disease persistence and extinction, with outcomes linked to the basic reproduction number. A numerical approach was employed to facilitate computational analysis, and simulations were conducted using data from existing literature to generate realistic predictions. The stochastic model was further evaluated against its deterministic counterpart to assess predictive accuracy. The results highlight the significant role of randomness in epidemiological dynamics, providing valuable insights into disease spread and control strategies.
- infectious disease,
- stochastic model,
- persistence,
- existence,
- simulation
Citation: Shah Hussain, Naveed Iqbal, Elissa Nadia Madi, Mohsen Bakouri, Ilyas Khan, Wei Sin Koh. On the stochastic modeling and forecasting of the $ \mathscr{SVIR} $ epidemic dynamic model under environmental white noise[J]. AIMS Mathematics, 2025, 10(2): 3983-3999. doi: 10.3934/math.2025186

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Abstract

This study introduced a novel $ \mathscr{SVIR} $ epidemic model incorporating environmental white noise to account for stochastic fluctuations in disease transmission. The model was analyzed to determine conditions for disease persistence and extinction, with outcomes linked to the basic reproduction number. A numerical approach was employed to facilitate computational analysis, and simulations were conducted using data from existing literature to generate realistic predictions. The stochastic model was further evaluated against its deterministic counterpart to assess predictive accuracy. The results highlight the significant role of randomness in epidemiological dynamics, providing valuable insights into disease spread and control strategies.

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