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Cited by 9COVID-19 epidemiological studiesMathematical and Theoretical Epidemiology and Ecology ModelsModel Reduction and Neural Networks

System Inference Via Field Inversion for the Spatio-Temporal Progression of Infectious Diseases: Studies of COVID-19 in Michigan and Mexico

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Wang, Zhenlin, Carrasco-Teja, Mariana, Zhang, Xiaoxuan, Teichert, Gregory H., Garikipati, Krishna·2021·Archives of Computational Methods in Engineering
DOI 10.1007/s11831-021-09643-1PMC PMC8484856

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Abstract

We present an approach to studying and predicting the spatio-temporal progression of infectious diseases. We treat the problem by adopting a partial differential equation (PDE) version of the Susceptible, Infected, Recovered, Deceased (SIRD) compartmental model of epidemiology, which is achieved by replacing compartmental populations by their densities. Building on our recent work (Computat Mech 66:1177, 2020), we replace our earlier use of global polynomial basis functions with those having local support, as epitomized in the finite element method, for the spatial representation of the SIRD parameters. The time dependence is treated by inferring constant parameters over time intervals that coincide with the time step in semi-discrete numerical implementations. In combination, this amounts to a scheme of field inversion of the SIRD parameters over each time step. Applied to data over ten months of 2020 for the pandemic in the US state of Michigan and to all of Mexico, our system inference via field inversion infers spatio-temporally varying PDE SIRD parameters that replicate the progression of the pandemic with high accuracy. It also produces accurate predictions, when compared against data, for a three week period into 2021. Of note is the insight that is suggested on the spatio-temporal variation of infection, recovery and death rates, as well as patterns of the population's mobility revealed by diffusivities of the compartments. Supplementary information The online version contains supplementary material available at 10.1007/s11831-021-09643-1.

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  • There exist models that have considered density-dependent effects on migration and on cell proliferation.

    “There exist models that have considered density-dependent effects on migration, for instance representing cells interacting with each other, and on cell proliferation, for instance, modeling its saturation at high cell density8,27.”

    From Inference of weak-form partial differential equations describing migration and proliferation mechanisms in wound healing experiments on cancer cells (2025) · cites this paper as [27]

    The Introduction and Results discuss population-density gradients and mobility in a COVID-19 model, not cell migration or proliferation. Searches for density-dependent migration, cell interactions, and proliferation saturation found no passage in our copy addressing the attributed claim. (LLM, conf=0.74)

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Cited by

Sorted by citations

Authors
Wang, Z., Carrasco-Teja, M., Zhang, X., Teichert, G. H., & Garikipati, K.
Affiliations
University of Michigan (US)
Corresponding author
Garikipati, Krishna
ORCID
Venue
Archives of Computational Methods in Engineering
Publisher
Springer Science and Business Media LLC
Published
2021-10
Volume
28
Issue
6
Pages
4283-4295
ISSN
  • 1134-3060 (ISSN-L)
  • 1886-1784
DOI
10.1007/s11831-021-09643-1
PMC
PMC8484856
OpenAlex
W3201781889
Cited by
9
References
2
Citations by year
2026: 1 · 2025: 5 · 2024: 2 · 2022: 1
FWCI
0.29
Type
journal article
Language
en
Open access
Licence
Locations
  • Archives of Computational Methods in Engineering (publishedVersion, public-domain)
  • medRxiv (acceptedVersion, cc-by-nc-nd)
  • PubMed Central (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University) (cc-by)
Funders
Defense Advanced Research Projects Agency (HR001119900)
Topics
  • Physical Sciences › Mathematics › Modeling and Simulation › COVID-19 epidemiological studies
  • Health Sciences › Medicine › Public Health, Environmental and Occupational Health › Mathematical and Theoretical Epidemiology and Ecology Models
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Model Reduction and Neural Networks
Keywords
COVID-19 pandemic, SIRD model, parameter inference, field inversion, compartmental model, finite element analysis, movement patterns, diffusion coefficient, epidemic forecasting, Michigan, Mexico

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