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.D7.4
Abstract: D7.00004 : Forecasting fluctuating outbreaks in seasonally driven epidemics
4:18 PM–4:54 PM
Preview Abstract
Abstract
Author:
Lewi Stone
(Tel Aviv University)
Seasonality is a driving force that has major impact on the
spatio-temporal dynamics of natural systems and their
populations. This is especially true for the transmission of
common infectious diseases such as influenza, measles,
chickenpox, and pertussis. Here we gain new insights into the
nonlinear dynamics of recurrent diseases through the analysis of
the classical seasonally forced SIR epidemic model. Despite many
efforts over the last decades, it has been difficult to gain
general analytical insights because of the complex
synchronization effects that can evolve between the external
forcing and the model's natural oscillations. The analysis
advanced here attempts to make progress in this direction by
focusing on the dynamics of ``skips'' where we identify and
predict years in which the epidemic is absent rather than
outbreak years. Skipping events are intrinsic to the forced SIR
model when parameterised in the chaotic regime. In fact, it is
difficult if not impossible to locate realistic chaotic parameter
regimes in which outbreaks occur regularly each year. This
contrasts with the well known Rossler oscillator whose outbreaks
recur regularly but whose amplitude vary chaotically in time
(Uniform Phase Chaotic Amplitude oscillations). The goal of the
present study is to develop a ``language of skips'' that makes it
possible to predict under what conditions the next outbreak is
likely to occur, and how many ``skips'' might be expected after
any given outbreak. We identify a new threshold effect and give
clear analytical conditions that allow accurate predictions.
Moreover, the time of occurrence (i.e., phase) of an outbreak
proves to be a useful new parameter that carries important
epidemiological information. In forced systems, seasonal changes
can prevent late-initiating outbreaks (i.e., having high phase)
from running to completion. These principles yield forecasting
tools that should have relevance for the study of newly emerging
and reemerging diseases.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2009.MAR.D7.4