https://doi.org/10.1140/epjp/s13360-025-06443-5
Regular Article
A nontrivial beneficial aspect of predation-driven Allee effect in an eco-epidemiological model
1
Department of Mathematics, Techno India University, Sector-V, Salt Lake, 700091, Kolkata, West Bengal, India
2
Department of Mathematics, Bankura University, 722155, Bankura, West Bengal, India
3
Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B. T. Road, 700108, Kolkata, India
Received:
7
April
2025
Accepted:
19
May
2025
Published online:
12
June
2025
In this study, we focus on integrating two crucial biological factors—the Allee effect and disease—into a predator–prey model using a Holling type-II functional response. Our investigation explores scenarios where the Allee effect is driven by predation. While there have been limited studies on predator–prey systems incorporating a predation-driven Allee effect, none have yet explored the influence of diseases within such systems. This research marks the inaugural effort in this direction, particularly focusing on eco-epidemiological systems. We conduct a comprehensive analysis, starting with the local stability of equilibrium points and the analysis of Hopf bifurcations around the endemic equilibrium point. Our numerical simulations reveal that the eco-epidemiological system, without the Allee effect, displays chaos arising from a stable focus for the force of infection, while it exhibits a stable solution in the presence of the predator-driven Allee effect. We have a natural understanding that in the presence of the Allee effect, the fitness of the species will be reduced at low population density. But we have a nontrivial result that predator-driven Allee effects reduce the chance of chaotic dynamics, which is no doubt beneficial for the system. As the force of infection increases, the system undergoes diverse manifestations of bi-stability and tri-stability behavior, coexisting with susceptible prey-only equilibrium state, predator-free co-existence state, all species co-existence state, oscillatory co-existence state, predator-free oscillatory co-existence state, and the prospect of all species extinction state. Due to the model’s heightened sensitivity to initial conditions, we construct basin of attraction diagrams for the bi-stability and tri-stability regions. Under heightened disease prevalence, two pivotal outcomes emerge: Either the entire population succumbs to extinction within the system, or the predator population gradually diminishes and eventually vanishes due to inadequate biomass from the infected prey population. Our research has the potential to enhance the field of the Allee effect and contribute to a better understanding of predator–prey interactions in naturalistic environments.
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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.
