Data-Driven Partial Differential Equations for Simulating Epidemic Spread and Containment Strategies

The global surge in infectious diseases has underscored the urgent need for accurate, adaptable, and predictive models to inform public health decision-making.Traditional compartmental models, while foundational in epidemiology, often fail to capture the spatial heterogeneity and time-varying dynamics of real-world outbreaks.In response, the integration of data-driven partial differential equations (PDEs) has emerged as a transformative approach for simulating epidemic spread with enhanced spatiotemporal resolution.By combining mechanistic modeling with real-time data, PDE-based frameworks provide a mathematically rigorous yet flexible means to model diffusion, reaction, and mobility-driven transmission patterns across diverse geographic and demographic landscapes.This article presents a comprehensive review and practical implementation of data-driven PDEs for modeling epidemic dynamics.It begins with a theoretical overview of diffusion-reaction PDE systems and their relevance to infectious disease modeling.We then explore how machine learning algorithms, remote sensing data, and mobility datasets are integrated to estimate model parameters dynamically and adapt to changing epidemiological contexts.Case studies are examined across various diseases, including COVID-19 and dengue fever, highlighting how PDE models can simulate outbreak trajectories, healthcare resource demands, and the localized effectiveness of containment strategies such as lockdowns, vaccination, and contact tracing.Special attention is given to the computational challenges and interpretability concerns of PDE calibration in high-dimensional, data-sparse environments.The article concludes with forwardlooking perspectives on combining PDE modeling with reinforcement learning and agent-based models for optimizing real-time policy interventions.This synthesis positions data-driven PDEs as a vital tool in the modern epidemiologist's toolkit for guiding evidencebased, spatially-aware containment strategies in future public health crises.