Spectral properties of the connectivity matrix and the SIS-epidemic threshold for mid-size metapopulations

Abstract. We consider the spread of an infectious disease on a heterogeneous metapopulation defined by any (correlated or uncorrelated) network. The infection evolves under transmission, recovery and migration mechanisms. We study some spectral properties of a connectivity matrix arising from the continuous-time equations of the model. In particular we show that the classi-cal sufficient condition of instability for the disease-free equilibrium, well known for the partic-ular case of uncorrelated networks, works also for the general case. We give also an alternative condition that yields a more accurate estimation of the epidemic threshold for correlated (either assortative or dissortative) networks. Key words: SIS epidemic, complex network