  This paper introduces an innovative model for infectious diseases in
predator-prey populations. We not only prove the existence of global
non-negative solutions but also establish essential criteria for the system's
decline and sustainability. Furthermore, we demonstrate the presence of a Borel
invariant measure, adding a new dimension to our understanding of the system.
To illustrate the practical implications of our findings, we present numerical
results. With our model's comprehensive approach, we aim to provide valuable
insights into the dynamics of infectious diseases and their impact on
predator-prey populations.
