We investigate eco-epidemic models to analyze the averaged dynamics of spatio-temporal systems. Specifically, we study a coupled Lotka–Volterra–Susceptible–Infected–Susceptible model with diffusion, posed on various graph structures. This eco-epidemic framework, formulated as ordinary differential equations on graphs (Graph ODEs), consists of four equations describing the evolution of susceptible and infected prey and predator populations, capturing ecological interactions, disease transmission, and spatial dispersal on a graph. Our primary goal is to understand how spatial coupling influence the system’s averaged temporal dynamics. Numerical experiments demonstrate that diffusion strength has a significant impact on the temporal behavior, underscoring the crucial role of spatial processes in shaping eco-epidemic dynamics.