THERMAL SCIENCE

International Scientific Journal

Armughan Ayaz

,

Thoraya N. Alharthi

,

Aziz Ur Muhammad

,

Ghada R. Elnaggar

,

Muhammad Rafiq

,

Zafar Iqbal

,

Nauman Ahmed

,

Ali Akgul

,

Ilyas Khan

MATHEMATICAL AND NUMERICAL INVESTIGATIONS OF FRACTIONAL STOCHASTIC EPIDEMIC MODEL

ABSTRACT
Sexually transmitted diseases are infectious diseases and a significant threat to human health. In this work, a standard integer-order model of Chlamydia is transformed into a fractional-order stochastic mathematical model. The steady-state of the continuous system is determined and considered for disease forecasting and stability analysis. The fractional stochastic system is tested for stability at both equilibrium states by following the classical Jacobian matrix theory. It is investigated the underlying epidemic model has a unique solution. The non-negative and bounded solutions of the model also provide a deeper understanding of the disease propagation. Then, a finite difference numerical algorithm is constructed for approximating the solution. To assess the efficiency of the algorithm, non-negativity and boundedness of the numerical method are investigated. Furthermore, the algorithm is applied to a test example to obtain the simulated graphs. Ultimately, the study's outcomes are summarized in the form of conclusions.
KEYWORDS
fractional differential equation, stochastic process, chlamydia disease, Lyapunov function, GL-NSFD scheme, stability
PAPER SUBMITTED: 2024-12-02
PAPER REVISED: 2025-02-10
PAPER ACCEPTED: 2025-04-30
PUBLISHED ONLINE: 2025-09-26
DOI REFERENCE: https://doi.org/10.2298/TSCI2505669A
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2025, VOLUME 29, ISSUE Issue 5, PAGES [3669 - 3679]
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Mathematical and numerical investigations of fractional stochastic epidemic model

2025 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence