https://doi.org/10.1140/epjp/s13360-025-06225-z
Regular Article
Dynamical study of a fear-influenced fractional predator–prey model with disease spread
Department of Mathematics, Guru Ghasidas Vishwavidyalaya (A Central University), 495009, Bilaspur, India
Received:
8
February
2025
Accepted:
17
March
2025
Published online:
15
April
2025
Recent field studies on vertebrates indicate that predator presence not only influences prey demographics but also induces behavioral adaptations driven by fear. These adaptations often enhance prey survival while reducing reproductive success. Inspired by these observations, we develop and analysis mathematical models that incorporate fear effects into predator–prey dynamics. In this study, we investigate a fractional-order three-species predator–prey system, expanding upon the model proposed by Kankan Sarkar and Subhas Khanjanchi (Chaos: Interdiscip. J. Nonlinear Sci. 32:083126, 2022). The total population is divided into three categories: prey, susceptible prey, and infected prey. Additionally, the impact of predator-induced fear on prey behavior is considered. We analysis the existence, uniqueness, and boundedness of solutions using the inverse Laplace transform and the Mittag-Leffler function. The local and global stability of equilibrium points is examined under different conditions. Moreover, we explore the Lyapunov function, fractional derivatives, and Hopf bifurcation at the interior equilibrium point. To approximate solutions, LaSalle’s Invariance Principle is applied. Numerical simulations and graphical illustrations, conducted using Python, confirm the theoretical findings for both models.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
