Analysis, Estimation, and Validation of Discrete-Time Epidemic Processes

Philip E. Pare, Ji Liu, Carolyn L. Beck, Barrett E. Kirwan, Tamer Basar

Research output: Contribution to journalArticle

Abstract

Models of spreading processes over nontrivial networks are commonly motivated by modeling and analysis of biological networks, computer networks, and human contact networks. However, learning the spread parameters of such models has not yet been explored in detail, and the models have not been validated by real data. In this paper, we present several different spread models from the literature and explore their relationships to each other; for one of these processes, we present a sufficient condition for asymptotic stability of the healthy equilibrium, show that the condition is necessary and sufficient for uniqueness of the healthy equilibrium, and present necessary and sufficient conditions for estimating the spread parameters. Finally, we employ two real data sets, one from John Snow's seminal work on cholera epidemics in London in the 1850s and the other one from the United States Department of Agriculture, to validate an approximation of a well-studied network-dependent susceptible-infected-susceptible model.

Original languageEnglish (US)
Article number8488684
Pages (from-to)79-93
Number of pages15
JournalIEEE Transactions on Control Systems Technology
Volume28
Issue number1
DOIs
StatePublished - Jan 2020

Fingerprint

Snow
Asymptotic stability
Computer networks
Agriculture

Keywords

  • Epidemic processes
  • John Snow's cholera data set
  • networked control systems
  • nonlinear systems
  • system identification in biomedical applications
  • validation of networked systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

Cite this

Analysis, Estimation, and Validation of Discrete-Time Epidemic Processes. / Pare, Philip E.; Liu, Ji; Beck, Carolyn L.; Kirwan, Barrett E.; Basar, Tamer.

In: IEEE Transactions on Control Systems Technology, Vol. 28, No. 1, 8488684, 01.2020, p. 79-93.

Research output: Contribution to journalArticle

@article{6c62a94babc244c3a8af4306db0bacac,
title = "Analysis, Estimation, and Validation of Discrete-Time Epidemic Processes",
abstract = "Models of spreading processes over nontrivial networks are commonly motivated by modeling and analysis of biological networks, computer networks, and human contact networks. However, learning the spread parameters of such models has not yet been explored in detail, and the models have not been validated by real data. In this paper, we present several different spread models from the literature and explore their relationships to each other; for one of these processes, we present a sufficient condition for asymptotic stability of the healthy equilibrium, show that the condition is necessary and sufficient for uniqueness of the healthy equilibrium, and present necessary and sufficient conditions for estimating the spread parameters. Finally, we employ two real data sets, one from John Snow's seminal work on cholera epidemics in London in the 1850s and the other one from the United States Department of Agriculture, to validate an approximation of a well-studied network-dependent susceptible-infected-susceptible model.",
keywords = "Epidemic processes, John Snow's cholera data set, networked control systems, nonlinear systems, system identification in biomedical applications, validation of networked systems",
author = "Pare, {Philip E.} and Ji Liu and Beck, {Carolyn L.} and Kirwan, {Barrett E.} and Tamer Basar",
year = "2020",
month = "1",
doi = "10.1109/TCST.2018.2869369",
language = "English (US)",
volume = "28",
pages = "79--93",
journal = "IEEE Transactions on Control Systems Technology",
issn = "1063-6536",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "1",

}

TY - JOUR

T1 - Analysis, Estimation, and Validation of Discrete-Time Epidemic Processes

AU - Pare, Philip E.

AU - Liu, Ji

AU - Beck, Carolyn L.

AU - Kirwan, Barrett E.

AU - Basar, Tamer

PY - 2020/1

Y1 - 2020/1

N2 - Models of spreading processes over nontrivial networks are commonly motivated by modeling and analysis of biological networks, computer networks, and human contact networks. However, learning the spread parameters of such models has not yet been explored in detail, and the models have not been validated by real data. In this paper, we present several different spread models from the literature and explore their relationships to each other; for one of these processes, we present a sufficient condition for asymptotic stability of the healthy equilibrium, show that the condition is necessary and sufficient for uniqueness of the healthy equilibrium, and present necessary and sufficient conditions for estimating the spread parameters. Finally, we employ two real data sets, one from John Snow's seminal work on cholera epidemics in London in the 1850s and the other one from the United States Department of Agriculture, to validate an approximation of a well-studied network-dependent susceptible-infected-susceptible model.

AB - Models of spreading processes over nontrivial networks are commonly motivated by modeling and analysis of biological networks, computer networks, and human contact networks. However, learning the spread parameters of such models has not yet been explored in detail, and the models have not been validated by real data. In this paper, we present several different spread models from the literature and explore their relationships to each other; for one of these processes, we present a sufficient condition for asymptotic stability of the healthy equilibrium, show that the condition is necessary and sufficient for uniqueness of the healthy equilibrium, and present necessary and sufficient conditions for estimating the spread parameters. Finally, we employ two real data sets, one from John Snow's seminal work on cholera epidemics in London in the 1850s and the other one from the United States Department of Agriculture, to validate an approximation of a well-studied network-dependent susceptible-infected-susceptible model.

KW - Epidemic processes

KW - John Snow's cholera data set

KW - networked control systems

KW - nonlinear systems

KW - system identification in biomedical applications

KW - validation of networked systems

UR - http://www.scopus.com/inward/record.url?scp=85054680664&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85054680664&partnerID=8YFLogxK

U2 - 10.1109/TCST.2018.2869369

DO - 10.1109/TCST.2018.2869369

M3 - Article

AN - SCOPUS:85054680664

VL - 28

SP - 79

EP - 93

JO - IEEE Transactions on Control Systems Technology

JF - IEEE Transactions on Control Systems Technology

SN - 1063-6536

IS - 1

M1 - 8488684

ER -