Automated Discovery of Spatio-Temporal Epidemic Patterns via Hybrid Evolutionary-PDE Frameworks

Abstract

We introduce a hybrid computational framework for the automated discovery of complex dynamic regimes in spatially distributed epidemiological models. Traditional models often fail to capture the rich spatio-temporal heterogeneity of disease spread, while high-dimensional Partial Differential Equation (PDE) models suffer from the “curse of dimensionality” during parameter calibration. To address this, we couple a Differential Evolution (DE) search engine with a Just-In-Time (JIT) compiled Finite Difference solver, resulting in a hybrid architecture that performs “Simulation-Based Inference”. This method navigates the parameter space to identify regimes that generate specific emergent behaviors, such as Turing patterns, traveling wave competition, and resonance-driven outbreaks. We apply our method to a spatial Susceptible-Infected-Recovered-Susceptible (SIRS) model featuring seasonal forcing and heterogeneous diffusion. Our results demonstrate that the JIT-compiled solver achieves a $\sim 9 \times$ speedup compared to vectorized NumPy implementations, rendering the evolutionary exploration of PDEs computationally feasible and validating the system's ability to discover worst-case epidemic scenarios and geometric interference patterns without reliance on manual analytical derivation.