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This paper introduces an innovative model for infectious diseases inpredator-prey populations. We not only prove the existence of globalnon-negative solutions but also establish essential criteria for the system'sdecline and sustainability. Furthermore, we demonstrate the presence of a Borelinvariant measure, adding a new dimension to our understanding of the system.To illustrate the practical implications of our findings, we present numericalresults. With our model's comprehensive approach, we aim to provide valuableinsights into the dynamics of infectious diseases and their impact onpredator-prey populations.

Dynamics of infectious diseases in predator-prey populations: a stochastic model, sustainability, and invariant measure