Epidemic dynamics in the spatio-temporal predator-prey model

In this work, we develop a novel mathematical model to simulate the spatio-temporal dynamics of epidemics in a predator–prey system. The model integrates the classical Lotka–Volterra predator–prey framework with a Susceptible–Infected–Susceptible disease model and explicitly incorporates diffusion terms to capture spatial movement. This unified approach allows us to simultaneously analyze susceptible and infected prey and predator populations, and account for both ecological and spatial interactions. An extension beyond traditional models that often treat these processes separately. The model consists of four partial differential equations and includes key ecological factors such as growth and mortality rates, predation, reproduction, and carrying capacity. Through extensive numerical simulations across a wide range of ecological and epidemiological parameters, we systematically investigate how disease transmission and spatial diffusion shape population dynamics. The results reveal that spatial movement plays a critical role in determining species distribution and infection persistence, highlighting the complex interplay between disease spread and ecosystem stability.