On the fractional Wiener process and some stochastic epidemic models. | ||
| Alexandria Journal of Science and Technology | ||
| Articles in Press, Accepted Manuscript, Available Online from 18 October 2025 PDF (1.27 M) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/ajst.2025.393987.1075 | ||
| Authors | ||
| Aleya Abdelghany Lashen* 1; khairia El-said El-nady2; Mohamed Ahmed Morsi El-shindidy2 | ||
| 1Faculty of Science, Alexandria University, Egypt | ||
| 2Faculty of Science, Alexandria University, Egypt. | ||
| Abstract | ||
| This study develops a fractional stochastic framework for modeling epidemic spread, based on a recently proposed fractional Wiener process. The proposed model generalizes the classical SIR structure by incorporating fractional Brownian motion, which captures memory effects and long-range dependencies observed in real-world epidemiological data. The system is formulated through stochastic differential equations, using Itô stochastic calculus with fractional methods to describe transmission dynamics under uncertainty. The analysis addresses existence, uniqueness, and qualitative properties of the solutions to the fractional stochastic model. Numerical simulations are conducted to demonstrate the system's behavior under various conditions and to illustrate the role of stochastic fluctuations in epidemic progression. A variant of the model using a fractional Ornstein–Uhlenbeck process is also considered to assess the influence of damping and noise. The results highlight the effectiveness of the proposed framework in capturing complex epidemic behaviors and provide a mathematically robust approach for analyzing disease transmission. This work offers valuable insights for researchers and contributes to the broader development of stochastic modeling in epidemiology. | ||
| Keywords | ||
| Wiener Process; Fractional stochastic models; Stochastic integral epidemic model; SIR epidemic modeling; Fractional calculus | ||
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