2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009;
Pittsburgh, Pennsylvania
Session D7: Rare Events in Physics and Population Dynamics
2:30 PM–5:30 PM,
Monday, March 16, 2009
Room: 407
Sponsoring
Unit:
GSNP
Chair: Beate Schmittmann, Virginia Polytechnic Institute and State University
Abstract ID: BAPS.2009.MAR.D7.3
Abstract: D7.00003 : Fluctuations in epidemic modeling - disease extinction and control*
3:42 PM–4:18 PM
Preview Abstract
Abstract
Author:
Ira Schwartz
(U. S. Naval Research Laboratory)
The analysis of infectious disease fluctuations has recently
seen an increasing rise in the use of new tools and models from
stochastic
dynamics and statistical physics. Examples arise in modeling
fluctuations
of multi-strain diseases, in modeling adaptive social behavior and
its impact on disease fluctuations, and in the analysis of disease
extinction in finite population models. Proper stochastic model
reduction
[1] allows one to predict unobserved fluctuations from observed
data in multi-strain models [2]. Degree alteration and power law
behavior is predicted in adaptive network epidemic models [3,4].
And extinction rates derived from large fluctuation theory exhibit
scaling with respect to distance to the bifurcation point of disease
onset with an unusual exponent [5]. In addition to outbreak
prediction,
another main goal of epidemic modeling is one of eliminating the
disease
to extinction through various control mechanisms, such as vaccine
implementation or quarantine. In this talk, a description will be
presented of the fluctuational behavior of several epidemic models
and their extinction rates. A general framework and analysis of the
effect of non-Gaussian control actuations which enhance the rate to
disease extinction will be described. In particular, in it is shown
that even in the presence of a small Poisson distributed vaccination
program, there is an exponentially enhanced rate to disease
extinction.
These ideas may lead to improved methods of controlling disease where
random vaccinations are prevalent.
\\[4pt]
Recent papers:\\[0pt]
[1] E. Forgoston and I. B. Schwartz, ``Escape Rates
in a Stochastic Environment with Multiple Scales,'' arXiv:0809.1345
2008.\\[0pt]
[2] L. B. Shaw, L. Billings, I. B. Schwartz, ``Using dimension
reduction
to improve outbreak predictability of multi-strain diseases,'' J.
Math. Bio. {\bf 55}, 1 2007.\\[0pt]
[3] L. B. Shaw and I. B. Schwartz, ``Fluctuating epidemics on
adaptive
networks,'' Physical Review E {\bf 77}, 066101 2008.\\[0pt]
[4] L. B. Shaw and I. B. Schwartz, ``Noise induced dynamics in
adaptivenetworks with applications to epidemiology,''
arXiv:0807.3455 2008.\\[0pt]
[5] M. I. Dykman, I. B. Schwartz, A. S. Landsman, ``Disease
Extinction in the Presence of Random Vaccination,'' Phys. Rev.
Letts. {\bf 101}, 078101 2008.
*The author acknowledges support from ONR and ARO.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2009.MAR.D7.3