Modelling development of epidemics with dynamic small-world networks.

Saramaki J, Kaski K.

Laboratory of Computational Engineering, Helsinki University of Technology, P.O. Box 9203, FIN-02015 HUT, Finland.

We discuss the dynamics of a minimal model for spreading of infectious diseases, such as various types of influenza. The spreading takes place on a dynamic small-world network and can be viewed as comprising short- and long-range spreading processes. We derive approximate equations for the epidemic threshold as well as the spreading dynamics, and show that there is a good agreement with numerical discrete time-step simulations. We then analyse the dependence of the epidemic saturation time on the initial conditions, and outline a possible method of utilizing the model in predicting the development of epidemics based on early figures of infected. Finally, we compare time series calculated with our model to real-world data.