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Hamiltonian Analysis of Subcritical Stochastic Epidemic Dynamics
Joint Authors
Lietman, Thomas M.
Worden, Lee
Schwartz, Ira B.
Bianco, Simone
Porco, Travis C.
Ackley, Sarah
Source
Computational and Mathematical Methods in Medicine
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-08-28
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
We extend a technique of approximation of the long-term behavior of a supercritical stochastic epidemic model, using the WKB approximation and a Hamiltonian phase space, to the subcritical case.
The limiting behavior of the model and approximation are qualitatively different in the subcritical case, requiring a novel analysis of the limiting behavior of the Hamiltonian system away from its deterministic subsystem.
This yields a novel, general technique of approximation of the quasistationary distribution of stochastic epidemic and birth-death models and may lead to techniques for analysis of these models beyond the quasistationary distribution.
For a classic SIS model, the approximation found for the quasistationary distribution is very similar to published approximations but not identical.
For a birth-death process without depletion of susceptibles, the approximation is exact.
Dynamics on the phase plane similar to those predicted by the Hamiltonian analysis are demonstrated in cross-sectional data from trachoma treatment trials in Ethiopia, in which declining prevalences are consistent with subcritical epidemic dynamics.
American Psychological Association (APA)
Worden, Lee& Schwartz, Ira B.& Bianco, Simone& Ackley, Sarah& Lietman, Thomas M.& Porco, Travis C.. 2017. Hamiltonian Analysis of Subcritical Stochastic Epidemic Dynamics. Computational and Mathematical Methods in Medicine،Vol. 2017, no. 2017, pp.1-11.
https://search.emarefa.net/detail/BIM-1142116
Modern Language Association (MLA)
Worden, Lee…[et al.]. Hamiltonian Analysis of Subcritical Stochastic Epidemic Dynamics. Computational and Mathematical Methods in Medicine No. 2017 (2017), pp.1-11.
https://search.emarefa.net/detail/BIM-1142116
American Medical Association (AMA)
Worden, Lee& Schwartz, Ira B.& Bianco, Simone& Ackley, Sarah& Lietman, Thomas M.& Porco, Travis C.. Hamiltonian Analysis of Subcritical Stochastic Epidemic Dynamics. Computational and Mathematical Methods in Medicine. 2017. Vol. 2017, no. 2017, pp.1-11.
https://search.emarefa.net/detail/BIM-1142116
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1142116