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At a time when we are faced with so many
questions about severe acute respiratory syndrome (SARS), we must also
ask ourselves if the epidemic has reached its peak or not. Research carried
out by Frédéric Van Wijland(1) of the "Laboratoire
de Physique Théorique" (Theoretical Physics Laboratory, CNRS,
Université Paris Sud 11)(2) , shows how a theoretical field can
make an original contribution to this issue. This research makes it possible
to increase our in-depth knowledge of phenomena that appear to be highly
unrelated. For the researcher, there is a common point between sandpile
avalanches, autocatalytic reactions and how an epidemic spreads. All of
these phenomena are studied within the framework of "nonequilibrium"
systems. In other words, there is no general theory that describes the
different macroscopic states on the basis of microscopic data.
We are dealing here with concepts of thermodynamics
that focus on the macroscopic aspect of the behavior of matter (defined
by scientists in a "system") on the basis of its properties
(temperature, energy, etc.) or the microscopic aspect, by analyzing the
mechanisms of atoms in motion to understand the relationship between these
variables. Just as in the case of equilibrium systems (characterized by
continuous and constant variables), we can observe phase transitions or
changes in the state of "nonequilibrium" systems as well. And
in the case of an epidemic, it is a transition between a state where the
epidemic maintains itself indefinitely and a state where it dies out without
the possibility of resurfacing again. We refer here to the transition
of an active state (the epidemic in action, the avalanche in progress,
etc.) towards an absorbing state (complete disappearance of the infectious
agent, inert sandpiles, etc.).
One of the most commonly used modelling methods for epidemics consists
of dividing the population into two groups: infected (I) and healthy (H).
In the case of an infectious agent that is not deadly, the infected individuals
recover their health spontaneously after a predetermined amount of time
(I-->H). The infection of a healthy individual takes place during an
encounter with an infected individual (I+H-->I+I). In this problem,
we can observe that the epidemic will only spread if the population is
big enough and that it will die out on its own in the opposite case. Once
it has disappeared, it can never again come back. The scientist wanted
to understand exactly what happens when the population reaches the threshold
where the epidemic is on the verge of disappearing. It turns out that
in the case of this population density regime, certain types of behavior
emerge, known as universal in that they do not depend on the details of
the problem itself (speed at which individuals move from one place to
another, contamination rate, recovery speed, etc.). Other collective behaviors
also emerge in this regime that are difficult to understand. Basically,
everything must converge when the epidemic dies out. In a certain sense,
a piece of information passes through the population, whereas contact
occurs from one individual to the next in the contamination process; the
idea of complexity is demonstrated here. Frédéric Van Wijland
has identified these universal characteristics inherent in the propagation
of an epidemic and has shown that they are the same for other phenomena:
chemical autocatalysis problems (that lead to the poisoning of a surface,
for example) or the sandpile avalanche. The universal characteristics
are found in the way that the epidemic is spread or dies out, a system
in which individuals speak to each other from one end to the other of
the system.
The researcher determined an underlying critical point that, regardless
of the precise definitions of these different models, makes them remarkably
similar. This critical point is identical for the epidemic, the self-organized
criticability of the sandpile and some chemical reactions. The direct
consequence of its existence is that many do not depend on the microscopic
details that define the systems being studied. The idea of universality,
which we already knew was applicable to nonequilibrium phenomena, takes
on a new meaning here since it bridges the gab between several widely
unrelated fields, particularly epidemiology and self-organized criticability.
These results cast doubts on beliefs that have been widespread for a good
decade now.
1 - Physical Review Letters 89 (2002),
entitled "Universality Class of Nonequilibrium Phase Transitions
with Infinitely Many Absorbing States".
2 - Researcher at the Laboratoire de Physique Théorique of Orsay
(http://qcd.th.u-psud.fr/),
Frédéric Van Wijland is also a member of the research federation,
"Matière et Systèmes Complexes" (Complex Systems
and Matter, CNRS, Université de Paris 7), the physics center that
will be located at the new site of the Université de Paris 7 "Tolbiac
- Grands Moulins" in Paris (http://hogarth.pct.espci.fr/~jbf/msc/).
Researcher
contacts:
Frédéric Van Wijland, Laboratoire
de Physique Théorique
Tel: 00 31 30 253 28 33 or 00 31 30 271 12 36
E-mail: frederic.van-wijland@th.u-psud.fr
Alessandro Vespignani, Laboratoire de Physique Théorique
Tel: +33 1 69 15 82 12
CNRS Mathematics and Physical Sciences Department
contact:
Frederique Laubenheimer
Tel: +33 1 44 96 42 63
E-mail: frederique.laubenheimer@cnrs-dir.fr
Press
contact:
Magali Sarazin
Tel: +33 1 44 96 46 06
E-mail: magali.sarazin@cnrs-dir.fr
Paper: cond-mat/0209202
From: Frederic.Van-Wijland@th.u-psud.fr
(van wijland)
Date: Mon, 9 Sep 2002 11:19:18 GMT (10kb)
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