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
N1 - Funding Information:
Manuscript received November 1, 2017; revised May 17, 2018 and August 5, 2018; accepted August 12, 2018. Date of publication October 10, 2018; date of current version December 27, 2019. Manuscript received in final form September 4, 2018. This work was supported in part by USDA, CA, under Grant 58-6000-4-0028 and in part by the National Science Foundation under Grant CPS 1544953 and Grant ECCS 1509302. Recommended by Associate Editor G. Mercere. (Corresponding author: Philip E. Paré.) P. E. Paré, C. L. Beck, and T. Bas¸ar are with the Coordinated Science Laboratory, University of Illinois at Urbana–Champaign, Urbana, IL 61801 USA (e-mail: philip.e.pare@gmail.com; beck3@illinois.edu; basar1@illinois.edu).
Publisher Copyright:
© 1993-2012 IEEE.
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
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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 -