Utilizing memory effects to enhance resilience in disease-driven prey-predator systems under the influence of global warming

This research paper presents an eco-epidemiological model that investigates the intricate dynamics of a predator-prey system, considering the impact of fear-induced stress, hunting cooperation, global warming, and memory effects on species interactions. The model employs fractional-order derivatives to account for temporal dependencies and memory in ecological processes. By incorporating these factors, we aim to provide a more comprehensive understanding of the underlying mechanisms that govern the stability and behavior of ecological systems. Mathematically we investigate system's existence, equilibria and their stability. Moreover, global stability and hopf bifurcation also analyzed in this study. Numerical simulations have been performed to validate the analytical results. We find that the coexistence equilibrium is stable under specific conditions, along with the predator equilibrium and the disease-free equilibrium. Bifurcation analyses demonstrate the intricate behavior of species densities in response to changes in model parameters. Fear and global warming are found to stabilize the system, while cooperation and additional food for predators lead to destabilization. Additionally, the influence of species memory has been explored. We observe that memory tends to stabilize the system as species memory levels increase.