  I study the spreading of infectious diseases on heterogeneous populations. I
represent the population structure 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 analytical 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 on
heterogeneous populations.
