Pacific Institute for the Mathematical Sciences - PIMS

The underlying contact structure among individuals that determines the
pattern of disease transmission and the progression in time of this
pattern are two crucial elements in understanding and controlling
communicable disease spread within a social setting. Mathematical
models of infectious disease that are in principle analytically
tractable, have taken two general approaches in incorporating these
elements. The first approach, generally known as compartmental models,
addresses the time evolution of disease spread at the expense of
simplifying the pattern of transmission. On the other hand, the second
approach - contact networks - incorporates detailed information of
underlying contact structure among individuals. While providing
accurate estimates on the final size of outbreak/epidemics, this
approach in its current formalism, loses track of the time progression
of outbreaks. So far, the only alternative to integrate both aspects of
disease spread simultaneously, has been to abandon the analytical
approach and rely on computer simulations. Although, powerful modern
computers can perform an enormous amount of simulations at an
incredibly rapid pace, the complex structure of `realistic' contact
networks along with the stochastic nature of disease spread pose a
serious challenge to the ability of the computational techniques to the
robust analysis of disease spread in large populations in real time. An
analytical alternative to this approach is lacking. We offer a new
analytical framework, which incorporates both complexity of contact
network structure and time progression of disease spread. Furthermore,
we demonstrate that this framework works equally effective for finite-
and `infinite'-size networks.

IGTC Math Biology 2008