Single Infection Epidemic Spreading Model

It has been admitted, that the most appropriate models of epidemic spreading are those based on dynamical processes on particular graph models of networks, rather than those defined by phenomenological differential equations [1, 8]. Within this approach the nodes of a network are usually considered as individuals, who are connected with each other by vertices corresponding to social links. Although some authors use continuous time simulations (see e.g., [12]), the approach presented commonly (see [2] for a review) is based on the idea that at each discrete time step a particular node of the network can contaminate each of its neighbours with some finite probability p. The whole set of vertices is being divided into compartments, usually referred to susceptible (S), infected (I) and recovered (R) individuals, but the general mechanism stays more or less unchanged. There has been a broad range of methods developed in order to analyse such models. In the most basic approach people assume individuals to be identical and homogeneously mixed (homogeneous assumption [2]).