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

Document Type : Research Article

Authors

GAURAV SAINI ¹

BAPPA GHOSH ¹

SUNITA CHAND ²

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

² Department of Mathematics, Siksha `O' Anusandhan (Deemed to be University), India

10.22067/ijnao.2025.94352.1679

Abstract

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.

Keywords

Ebola virus

Fractional order model

Caputo derivative

L1 technique

Qualitative analysis

Subjects

• Numerical methods for differential equations and its applications

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