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math.DS2026
Constraint-Aware Physics-Informed Neural Networks for SEIR Reaction-Diffusion Epidemic Models with Vital Dynamics
Achraf Zinihi, Matthias Ehrhardt
Reaction-diffusion epidemic models with vital dynamics are an important framework for describing the spatial and temporal spread of infectious diseases. In this work, we present a…
math.DS2025
A Koopman Operator Framework for Nonlinear Epidemic Dynamics: Application to an SIRSD Model
Achraf Zinihi, Matthias Ehrhardt, Moulay Rchid Sidi Ammi
We develop and analyze an SIRSD epidemic model, which extends the classical SIR framework by incorporating waning immunity and disease-induced mortality. A rigorous well-posedness…
math.DS2025
Spatiotemporal SEIQR Epidemic Modeling with Optimal Control for Vaccination, Treatment, and Social Measures
Achraf Zinihi, Matthias Ehrhardt, Moulay Rchid Sidi Ammi
This paper introduces a spatiotemporal SEIQR epidemic model governed by a system of reaction-diffusion partial differential equations that incorporates optimal control strategies.…