Spatiotemporal dynamics of epidemics in one-dimensional networks with diffusion-mediated coupling

We investigate how spatial coupling mediated by a diffusing substance, modeled through chemical coupling, affects epidemic propagation in a one-dimensional network. Using the susceptible–infected–removed (SIR) epidemic model, we analyze how the coupling intensity 𝐷 and the interaction range 𝛾 influence the spatiotemporal spreading of the disease. The interactions between sites decay exponentially with distance, allowing a transition between predominantly local and long-range spreading regimes. Our results reveal the emergence of distinct propagation patterns associated with different coupling regimes. For weak coupling intensities, the epidemic front propagates gradually through the network, whereas strong coupling intensities produce a qualitatively different regime characterized by nonmonotonic advancement rates near the outbreak focus. We also show how the coupling parameters affect the average propagation velocity, the global infection peak, the extinction time, and the temporal variability of the epidemic. These findings demonstrate that the coupling structure plays a central role in shaping the spatial organization and temporal evolution of epidemic spread.