Qualitative and numerical analysis of a time-fractional Ebola model in population dynamics

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 24 آبان 1404

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.94352.1679

نویسندگان

GAURAV SAINI¹؛ BAPPA GHOSH^{* 2}؛ SUNITA CHAND³

¹Center for Data Science, Department of Computer Science and Engineering, Siksha `O' Anusandhan (Deemed to be University), India

²Center for Data Science, Department of Computer Science and Engineering, Siksha `O' Anusandhan (Deemed to be University), India

³Department of Mathematics, Siksha `O' Anusandhan (Deemed to be University), India

چکیده

Mathematical modeling of infectious diseases plays a vital role in understanding population dynamics and guiding control strategies. In this study, we formulate and analyze time-fractional Ebola virus model incorporating the Caputo derivative of order $\sigma \in (0,1)$ to capture memory and nonlocal effects in disease transmission. This formulation is important as it extends classical integer-order models to more realistically describe the persistence and delayed response of infection dynamics. A comprehensive qualitative analysis is presented, establishing the existence, uniqueness, and Hyers–Ulam stability of the solution of the considered model. To obtain the numerical approximation, a robust finite difference scheme based on the classical L1 discretization is developed. The resulting nonlinear system is efficiently solved using the Newton–Raphson iterative technique. The numerical results demonstrate that fractional-order models provide enhanced flexibility and accuracy compared to traditional integer-order formulations. Specifically, variation in the fractional order significantly influences the rate of infection and recovery, highlighting the crucial role of memory effects in epidemic modeling. These findings confirm that incorporating fractional derivatives offers improved insight into Ebola virus dynamics and can support more effective intervention and treatment strategies.

کلیدواژه‌ها

Ebola virus؛ Fractional order model؛ Caputo derivative؛ L1 technique؛ Qualitative analysis