Dynamics of a spatially explicit eco-epidemic model with double Allee effect

Abstract

This article deals with the dynamics of a reaction–diffusion eco-epidemic model that assimilates a double Allee effect. Allee effects are strongly related to extinction vulnerability of populations and two or more Allee effects can emerge simultaneously for the same population. Similarly, diseases can generate high mortality, decrease in reproduction rate, persistence, change in population size, etc. Surprisingly, relatively few studies capture the effect of both factors on a single population. Here we assume that susceptible prey populations suffer from both infectious and double Allee thresholds. We provide precise analysis of the proposed model, including (1) global existence of solutions; (2) the stability of positive constant solution; (3) sufficient conditions leading to Turing instabilities. We also conduct a thorough analysis of the associate local (ODE) system to enhance understanding of the effects of Allee and diffusion on the stability of the steady-state solution. The direction and stability of Hopf-bifurcation are analyzed for the local system concerning the Allee parameter. We have derived conditions for the occurrence of the overexploitation phenomenon, also demonstrated this through simulation. We emanate the pseudo-disease-free subsystem numerically with various dynamics related to the Allee threshold. Also this study shows that both Allee thresholds can generate chaotic dynamics. A brief simulation is performed to explain the developments of the pattern and its mechanism. Furthermore, we see that both weak and strong Allee effects can show enriched pattern diagrams.