Speaker
Description
Eco-epidemic systems offer a fundamental framework for examining the interaction between predator–prey dynamics and infectious disease transmission. Motivated by the European rabbit–Iberian lynx system, we extend the model in \cite{upadhyay2016wave} by incorporating a nonlinear predator-induced fear function that captures immediate behavioral responses and memory-driven carryover effects \cite{wang2016modelling, o2014biological}. The resulting reaction–diffusion model describes susceptible prey, infected prey, and predator populations under zero-flux boundary conditions. In the absence of diffusion, the temporal system exhibits saddle-node, Hopf, and cusp bifurcations with respect to the fear parameter. The analysis reveals contrasting roles of fear and carryover: increasing fear can destabilize the coexistence equilibrium and generate oscillatory outbreaks, whereas stronger carryover effects enhance stabilization and species persistence. Analytical results on local and global stability are supported by simulations. With diffusion, the system undergoes Turing instability, producing spatiotemporal structures including clustered patterns, spirals, and wave-like chaotic dynamics. Lower levels of fear and carryover amplify spatial heterogeneity and disease spread. These findings demonstrate that predator-induced fear and its carryover effects shape ecosystem stability, pattern formation, and epidemiological outcomes, providing insight into fear-mediated eco-epidemic dynamics.
Bibliography
@article{upadhyay2016wave,
title={Wave of chaos in a spatial eco-epidemiological system: Generating realistic patterns of patchiness in rabbit--lynx dynamics},
author={Upadhyay, Ranjit Kumar and Roy, Parimita and Venkataraman, Chandrasekhar and Madzvamuse, Anotida},
journal={Mathematical Biosciences},
volume={281},
pages={98--119},
year={2016},
publisher={Elsevier}
}
@article{o2014biological,
title={Biological carryover effects: linking common concepts and mechanisms in ecology and evolution},
author={O'Connor, Constance M and Norris, D Ryan and Crossin, Glenn T and Cooke, Steven J},
journal={Ecosphere},
volume={5},
number={3},
pages={1--11},
year={2014},
publisher={Wiley Online Library}
}
@article{wang2016modelling,
title={Modelling the fear effect in predator--prey interactions},
author={Wang, Xiaoying and Zanette, Liana and Zou, Xingfu},
journal={Journal of mathematical biology},
volume={73},
number={5},
pages={1179--1204},
year={2016},
publisher={Springer}
}
