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Chapter 18
Interplay of Network State and Topology in Epidemic Dynamics
Thilo Gross
Max-Planck Institute for the Physics of Complex Systems,
Nothnitzer Strae 38, 01187 Dresden, Germany
18.1. Introduction
Throughout history epidemic diseases have been a constant threat to humans
(Cartwright, 1972; Oldstone, 1998). There is evidence that even our earliest ances-
tors suered from disease-related mortality (Hart, 1983). Many of the old diseases
have by now become harmless childhood maladies or have disappeared entirely.
However, as humankind prospered and spread out new epidemic diseases continued
to arrive in the human population (Karlen, 1995). The extend to which epidemic
diseases have shaped our culture and politics can be guessed from religious texts,
which contain numerous references to epidemics and rules for their avoidance.
In the 20th century we have witnessed a brief episode in which it seemed
that mankind was about to win the struggle and free itself from epidemics. The
widespread use of antibiotics drove many infectious diseases back to hiding places in
remote locations and animal populations (so-called disease vectors). Some sources
hold that the second world war was the rst major war in history in which far
more lives were lost due to ghting than epidemics (Karlen, 1995). But, even when
the belief that biomedical progress would conquer epidemics was still widespread,
there was evidence to the contrary: In the 1950 new hemorrhagic fevers appeared in
several parts of the world (Daubney et al., 1993). The subsequent decades brought
Legionnaires disease (Breiman et al., 1990), Ebola fever (Bowen et al., 1977) and
a return of syphilis (Sell and Norris, 1983; Grassly et al., 2005). Nevertheless, the
awareness to epidemic diseases remained low until AIDS appeared in the 1980s
(Grmek, 1990). Since then new diseases, such as SARS (Omi, 2006) and ESME
(Haglund and Gunther, 2003), have emerged and old killers, such as Malaria (Pam-
pana and Russel, 1955), Tuberculosis (Bloom and Christopher, 1992) and Inuenza
(Kilbourne, 1987), have returned; some of them in new forms.
At present old and new diseases seem to arrive at a increasing rate. Apart
from increased attention in the media, there are several fundamental reasons for
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