Multi-fidelity methods for kinetic models of epidemic dynamics with uncertain contact structure
In this work, we develop a multi-fidelity strategy for kinetic models in epidemiology with uncertain contact dynamics. Assessing and controlling the population-level effects of contact dynamics requires the development of models for understanding observable effects of heterogeneous contact structures, whose formation depends on complex social phenomena. These can be captured taking into account high-dimensional uncertain quantities. The proposed approach combines high-fidelity kinetic solvers with a hierarchy of low-fidelity surrogates, including reduced macroscopic models and coarse kinetic descriptions, remaining applicable even in regimes where a macroscopic closure is unavailable. This hierarchical framework identifies representative parameter samples and reconstructs full solutions via projection-based techniques, enabling efficient uncertainty propagation while drastically reducing computational cost. Numerical experiments in high-dimensional stochastic settings demonstrate that accurate statistical estimates of epidemic observables can be obtained with significantly reduced computational costs compared to standard approaches.