A bi-fidelity collocation approach for kinetic epidemic models with random inputs

Data uncertainty is certainly one of the main problems in epidemiological modeling. The need for efficient methods capable of quantifying the effects of random inputs on outputs is essential to produce realistic scenarios of the spread of infection and to aim to implement the best control actions. In this work, we consider a bi-fidelity approach to quantify uncertainty in spatially dependent epidemic models. The approach is based on evaluating a high-fidelity model on a small number of samples appropriately selected on the basis of a large number of evaluations of a low-fidelity model, ensuring high computational efficiency and accuracy. In particular, we consider a class of multiscale kinetic transport models for high-fidelity reference and simple discrete-velocity kinetic models for low-fidelity evaluations. Both class of models share the same diffusive behavior and are solved numerically using methods that preserve their asymptotic limits, which permits to obtain stochastic asymptotic-preserving methods. A series of numerical experiments confirms the validity of the approach.