Separatrix reconstruction to identify tipping points in an eco-epidemiological model

Many ecological systems exhibit tipping points such that they suddenly shift from one state to another. These shifts can be devastating from an ecological point of view, and additionally have severe implications for the socio-economic system. They can be caused by overcritical perturbations of the state variables such as external shocks, disease emergence, or species removal. It is therefore important to be able to quantify the tipping points. Here we present a study of the tipping points by considering the basins of attraction of the stable equilibrium points. We address the question of finding the tipping points that lie on the separatrix surface, which partitions the space of system trajectories. We present an algorithm that reconstructs the separatrix by using a Moving Least Squares approximant based on radial basis functions. The algorithm is applied to an eco-epidemiological model of pack hunting predators that suffer disease infection. Our analysis reveals that strong hunting cooperation considerably promotes the survival of predators and renders the predators resilient to perturbations.