Laboratoire de Physique Théorique
Toulouse - UMR 5152

For along period of time Kermack McKendrick S.I.R. model has been used to study the diffusion of influenza like illness in a closed population. Individuals are divided in three compartments (Susceptible, Infectious and Recovered) and the dynamics of the epidemics is described in terms of a set of differential equation. The main assumption relies on the homogeneous mixing among individuals.

However recent works has shown contact network are highly heterogeneous and this fact has dramatically effects on the diffusions of epidemics. Many models have been developed to study the topological characteristics of network and how they influence the dynamics of the processes defined over them. In most of the cases, theoretical analysis has been limited to the study of static networks. This is a good approximation when we consider processes that operate on a time-scale much smaller than the network’s evolution. However, when the process has a time-scale comparable to that of the network’s evolution, for example in the cases of bluetooth worm diffusion, epidemics and rumors spreading, only numerical approaches are possible. In this talk I present some results from studies on the effects of contact heterogeneities on the diffusion of influenza like illness either at local either at world-wide scale. In the first case using synthetic populations that evaluate vaccine policy in an urban area. This approach uses an agent based model where individuals are endowed with demographic characteristics and a routine of activities drawn from surveys. Links among individuals are creating only when they share the same location at the same time. The model achieves a second-to-second timescale, thus network topology changes rapidly. This kind of representation is highly detailed and due to the absence of any a priori dynamic can be considered as a proxy to reality. In the second case, a more accurate meta-population model, that takes account of contact heterogeneities in a city, is used to study under which conditions an epidemic seeded in a city can spread through all the worldwide network.