  Two crucial elements facilitate the understanding and control of communicable
disease spread within a social setting. These components are, the underlying
contact structure among individuals that determines the pattern of disease
transmission; and the evolution of this pattern over time. Mathematical models
of infectious diseases, which are in principle analytically tractable, use two
general approaches to incorporate these elements. The first approach, generally
known as compartmental modeling, addresses the time evolution of disease spread
at the expense of simplifying the pattern of transmission. On the other hand,
the second approach uses network theory to incorporate detailed information
pertaining to the underlying contact structure among individuals. However,
while providing accurate estimates on the final size of outbreaks/epidemics,
this approach, in its current formalism, disregards the progression of time
during outbreaks. So far, the only alternative that enables the integration of
both aspects of disease spread simultaneously has been to abandon the
analytical approach and rely on computer simulations. We offer a new analytical
framework based on percolation theory, which incorporates both the complexity
of contact network structure and the time progression of disease spread.
Furthermore, we demonstrate that this framework is equally effective on finite-
and "infinite"-size networks. Application of this formalism is not limited to
disease spread; it can be equally applied to similar percolation phenomena on
networks in other areas in science and technology.
