Disease spreading in complex networks: A numerical study with Principal Component Analysis

Abstract

Disease spreading models need a population model to organize how individuals are distributed over space and how they are connected. Usually, disease agent (bacteria, virus) passes between individuals through these connections and an epidemic outbreak may occur. Here, complex networks models, like Erdös–Rényi, Small-World, Scale-Free and Barábasi–Albert will be used for modeling a population, since they are used for social networks; and the disease will be modeled by a SIR (Susceptible–Infected–Recovered) model. The objective of this work is, regardless of the network/population model, analyze which topological parameters are more relevant for a disease success or failure. Therefore, the SIR model is simulated in a wide range of each network model and a first analysis is done. By using data from all simulations, an investigation with Principal Component Analysis (PCA) is done in order to find the most relevant topological and disease parameters.