Stochastic asymptotic-preserving bi-fidelity method for multiscale spread of epidemics under uncertainty

Addressing data uncertainty is a key challenge in epidemiological modeling. To create realistic scenarios of infection spread and devise effective control measures, it is crucial to have effective techniques that can measure the impact of random inputs on model outcomes. In this study, we propose a bi-fidelity approach to quantify uncertainty in epidemic models with spatial dependencies. This approach involves employing a high-fidelity model on a limited number of carefully chosen samples, guided by numerous evaluations of a low-fidelity model, ensuring both computational efficiency and accuracy [Liu, Pareschi, Zhu, J. Comput. Phys. 2022]. Specifically, we focus on a class of multiscale kinetic transport models as high-fidelity reference [Bertaglia, Liu, Pareschi, Zhu, Netw. Heterog. Media 2022] and employ simpler discrete-velocity kinetic models for low-fidelity evaluations [Bertaglia, Pareschi, ESAIM: Math. Model. Numer. Anal. 2021]. Both model classes exhibit similar diffusive behaviors and are numerically solved using methods able to preserve their asymptotic limit, allowing to obtain stochastic asymptotic-preserving techniques. A series of numerical experiments demonstrates the soundness of the proposed approach.