Earthquakes can cause interconnected disruptions to the built environment, population health, emergency response systems, and community recovery, with consequences that may persist long after the initial seismic event. These post-earthquake dynamics are inherently time-dependent and may exhibit memory and hereditary effects that are not adequately represented by conventional integer-order differential equations. A physics-informed fractional framework was therefore developed to characterize the coupled evolution of post-earthquake disaster impacts and recovery processes. Five state variables were introduced to represent physical damage, population health burden, shelter demand, emergency response capacity, and community recovery. Their interactions were described through a coupled system of fractional-order differential equations. A physics-informed neural network was subsequently formulated by embedding the governing fractional-order equations and initial-condition constraints directly into the learning objective. Reference numerical trajectories were generated using the fractional Adams–Bashforth–Moulton method to assess the internal numerical consistency of the scenario-based simulations. Synthetic datasets informed by publicly available earthquake-related indicators were used to examine the computational behavior of the proposed framework under representative post-earthquake scenarios. The resulting formulation provides an integrated computational representation of the temporal dependencies among disaster impacts, public health burden, emergency response capacity, shelter demand, and community recovery while explicitly accounting for memory effects through fractional-order dynamics. The framework establishes a methodological basis for investigating post-earthquake system evolution and for examining how persistent disaster effects may influence recovery trajectories. Following validation against empirical observations from real earthquake events, the proposed approach could support scenario analysis, disaster preparedness, public health planning, emergency resource allocation, and quantitative assessment of post-earthquake recovery.
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