System inference for the spatio-temporal evolution of infectious diseases: Michigan in the time of COVID-19

Abstract

We extend the classical SIR model of infectious disease spread to account for time dependence in the parameters, which also include diffusivities. The temporal dependence accounts for the changing characteristics of testing, quarantine and treatment protocols, while diffusivity incorporates a mobile population. This model has been applied to data on the evolution of the COVID-19 pandemic in the US state of Michigan. For system inference, we use recent advances; specifically our framework for Variational System Identification (Wang et al., Comp. Meth. App. Mech. Eng., 356, 44-74, 2019; arXiv:2001.04816 [cs.CE]) as well as Bayesian machine learning methods.

Inference of deformation mechanisms and constitutive response of soft material surrogates of biological tissue by full-field characterization and data-driven variational system identification

“…This takes VSI out of the realm of linear regression to general nonlinear optimization in Algorithms 1 and 2. Furthermore, we have shown in recent work [39] that VSI and PDE-constrained optimization using adjoints also successfully infer spatiotemporally varying mechanisms and parameters. This result also is relevant to soft biological tissues with varying axes of symmetry.…”

“…materials [37,36,38], and recently used to explore identification of the canonical equations of infectious disease modelling [39]. Guided by the modern treatment of soft tissue continuum mechanics at finite strain, we have based our development of VSI on hyperelasticity.…”

“…Thus, we have exploited the understanding of steady state versus transient phenomena [36], and here we extend it to physical stability of the inferred model. In related research, we also have developed Bayesian approaches to quantify the uncertainty in the inferred physics [38], and techniques that account for spatial and temporal heterogeneity of the physical mechanisms [39]. In this communication, we apply VSI to infer, from a range of possible candidates, the mechanisms of deformation of soft polymeric materials from MR-u data.…”