Combining Coupled Skorokhod SDEs and Lattice Gas Frameworks for Multi-fidelity Modelling of Complex Behavioral Systems

TL;DR

This paper introduces a multi-fidelity modeling approach for complex behavioral systems with bio-social interactions, combining coupled Skorokhod SDEs and lattice gas models to quantify uncertainty in bounded domains with obstacles.

Contribution

It develops a novel multi-fidelity framework integrating stochastic differential equations and lattice gas simulations for behavioral systems with uncertainty quantification.

Findings

Effective modeling of epidemic healthcare systems with asymptomatic and susceptible populations.

Demonstrated the approach's ability to handle complex bounded domains with obstacles.

Provided numerical examples illustrating the methodology's applicability.

Abstract

To model reliably behavioral systems with complex bio-social interactions, accounting for uncertainty quantification, is critical for many application areas. However, in terms of the mathematical formulation of the corresponding problems, one of the major challenges is coming from the fact that corresponding stochastic processes should, in most cases, be considered in bounded domains, possibly with obstacles. This has been known for a long time and yet, very little has been done for the quantification of uncertainties in modelling complex behavioral systems described by such stochastic processes. In this paper, we address this challenge by considering a coupled system of Skorokhod-type stochastic differential equations (SDEs) describing interactions between active and passive participants of a mixed-population group. In developing a multi-fidelity modelling methodology for such behavioral systems, we combine low- and high-fidelity results obtained from (a) the solution of the underlying coupled system of SDEs and (b) simulations with a statistical-mechanics-based lattice gas model, where we employ a kinetic Monte Carlo procedure. Furthermore, we provide representative numerical examples of healthcare systems, subject to an epidemic, where the main focus in our considerations is given to an interacting particle system of asymptomatic and susceptible populations.