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 language | English (US) |
|---|---|
| Article number | 8488684 |
| Pages (from-to) | 79-93 |
| Number of pages | 15 |
| Journal | IEEE Transactions on Control Systems Technology |
| Volume | 28 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 2020 |
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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 journal › Article
}
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 -