Spreading dynamics on heterogeneous populations: multitype network approach.

I study the spreading of infectious diseases in heterogeneous populations. The population structure is described by a contact graph where vertices represent agents and edges represent disease transmission channels among them. The population heterogeneity is taken into account by the agent's subdivision in types and the mixing matrix among them. I introduce a type-network representation for the mixing matrix, allowing an intuitive understanding of the mixing patterns and the calculations. Using an iterative approach I obtain recursive equations for the probability distribution of the outbreak size as a function of time. I demonstrate that the expected outbreak size and its progression in time are determined by the largest eigenvalue of the reproductive number matrix and the characteristic distance between agents on the contact graph. Finally, I discuss the impact of intervention strategies to halt epidemic outbreaks. This work provides both a qualitative understanding and tools to obtain quantitative predictions for the spreading dynamics of heterogeneous populations.