Emerging Infectious Disease, Pandemic Preparedness and Mathematical Models: How to Prepare When We Don't Know the Enemy?

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.