Gaber, Taleb (2024) The Role of Refuge Prey and Allee Effect in Stabilizing an Eco-Epidemiological System With Non-Linear Incidence Rate. Masters thesis, Fakultas Sains dan Matematika Undip.

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Abstract

Eco-epidemiological models provide insights into factors influencing disease
transmission and host population stability. This study developed two eco-epidemiological
models to investigate the impacts of prey refuge availability and an Allee effect on
dynamics. Model A incorporated these mechanisms, while Model B did not. Both models
featured predator-prey and disease transmission and were analysed mathematically and
via simulation. Model equilibrium states were examined locally and globally under
differing parameter combinations representative of environmental scenarios. Model A
demonstrated globally stable conditions within certain parameter ranges, signalling
refuge and Allee effect terms promote robustness. Bifurcation analyses revealed
qualitative shifts in behaviour triggered by modifications like altering predator mortality
rate. Model A manifested a transcritical bifurcation indicating critical population
thresholds. An additional bifurcation type appeared when refuge and Allee stabilizing
impacts were absent in Model B. Findings showed disease burden and host persistence
positively associated with refuge habitat, reducing predator-prey encounters. High Allee
threshold had resultedin the extinction of the three species. Simulations aligned with
mathematical predictions. Model A underwent bifurcations at critical predator death rates
impacting prey outcomes. Insights into ecological tipping points enhance understanding
of managing wildlife infectious diseases amid changing environments. This work
provides a valuable framework to minimize transmission given resource availability or
demographic alterations, generating testable hypotheses.
Keywords: Allee Effect; Prey Refugee; Predator-Prey; Eco-Epidemiological Model;
Nonlinear Incidence Rate; Local Stability; Global Stability; Hopf Bifurcation;
Transcritical Bifurcation.

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