Untangling the role of tri-trophic food chain model in sustaining quokka population

Abstract

The introduction of predators like red fox and dingoes in the 1930s took a big toll on the quokka population. This paper is mainly concerned with designing conservation policies for quokka population (an endangered species). For this purpose, we designed a reaction–diffusion tri-tropic food chain model consisting quokka and its two predators, red fox and dingoes. We have shown the global existence, non-negativity and uniform boundedness for the designed spatiotemporal model. Existence and stability analysis of the equilibrium points for the model is done. We applied the prevalent idea of basic reproduction number with its origin from epidemiology to the food chain model, to deduce a condition for extinction and persistence of predator population. Natural systems exhibit an amazing diversity of structures in both living and non-living systems. We found that in the presence of diffusion, the model has the potential of exhibiting Turing instability generating beautiful patterns. Numerical results reveal that quokka tends to avoid places resided by dingoes. Our research aims at finding a solution for the current quokka extinction problem by showing the effect of presence of alternative food for dingoes and prohibiting the external factor causing death of quokka population.