Litvak-Hinenzon A., Stone L.
Epidemic waves, small worlds and targeted vaccination
(451K, PDF)

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.