Chytridiomycosis is the most significant reason for amphibian decline and extinction. It is caused by a fungal pathogen Batrachochytrium dendrobatidis (B d ) and affects many species of amphibians. This paper is mainly concerned with designing conservation policies for the frog population (corroboree, an endangered species), diminishing due to this disease. Our research aims at demonstrating mathematically and supporting the role of zooplankton as a potential biological control for B d . For this purpose, we designed a stochastic as well as diffusive ecoepidemic model consisting of B. dendrobatidis, frog, and zooplanktons. We have shown the global existence, nonnegativity, and long-term behavior for the designed stochastic model. Existence and stability analysis of the equilibrium points for the corresponding ODE and diffusive model is also done. We have also done bifurcation plotting for the ODE model and found the existence of Hopf bifurcation. We adopted the partial rank correlation coefficient (PRCC) to conduct global sensitivity analysis to estimate the most sensitive parameters responsible for disease prevalence and frog mortality. We provided a complete numerical analysis of our deterministic, stochastic, and diffusive models and compared the result. We found that the persistence and extinction of the frog population depend on the environmental stochasticity of zooplanktons. Numerical simulation of corresponding spatially explicit systems brings out complicated spatiotemporal dynamics, typically resulting in the formation of a patchy pattern. It also reveals that B d tends to decline in the places resided by zooplankton.
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.
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