4. Network Theory

Network Theory & Epidemic

The general understanding of non-equilibrium stochastic processes evolving on complex networks is an important challenge. In the frame- work of epidemiology, one of the key challenges is the identification and the understanding of the role of critical/vulnerable nodes in the diffusion process. Considering the SEIR model evolving on a complex networks, we present a study of the vulnerability.

The result presented here is based on simulations generated via EpiFast: an algorithm for stochastic disease propagation on complex networks. The latter network is evolving due to individual activties. This tool runs extremely fast for realistic simulations and allow us to consider large populations (millions of individuals and their heterogeneous details). Epifast is used as the major simulation engine to evaluate various interventions and to provide decision support for public health policy makers. Epifast is developed by the NDSSL Group at Virginia Tech.

The Vulnerability is a measure of how likely an individual is to get infected. Plotting this quantity  for each individual as a function of its degree and clustering coefficient, we generate a map on which on can “identified the more vulnerable nodes”. See below.

Vulenrability

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