Below is the ascii version of the abstract for 07-165.
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Litvak-Hinenzon A., Stone L.
Epidemic waves, small worlds and targeted vaccination
ABSTRACT. The success of an infectious disease to invade a population is strongly
controlled by the population's specific connectivity structure. Here a
network model is presented as an aid in understanding the role of social
behavior and heterogeneous connectivity in determining the
spatio-temporal patterns of disease dynamics . We explore the
controversial origins of long-term recurrent oscillations believed to be
characteristic to diseases that have a period of temporary immunity
after infection. In particular, we focus on sexually transmitted
diseases such as syphilis where this controversy is currently under
review. Although temporary immunity plays a key role, it is found that
in realistic small-world networks, the social and sexual behavior of
individuals also has great influence in generating long-term cycles. The
model generates circular waves of infection with unusual spatial
dynamics that depend on focal areas that act as pacemakers in the
population. Eradication of the disease can be efficiently achieved by
eliminating the pacemakers with a targeted vaccination scheme. A simple
difference equation model is derived, that captures the infection
dynamics of the network model and gives insights into their origins and
their eradication through vaccination.