Causal Tree of Disease Transmission and The Spreading of Infectious Diseases

We represent an epidemic outbreak by its causal tree of infection transmission, where nodes represent infected agents and arcs represent the disease transmission from an agent to another. The tree structure allows us to calculate different magnitudes quantifying the epidemic outbreak using iterative approaches. We focus on the expected outbreak size, and analyze its temporal evolution for different reproductive number and generation time distributions. We show that when the expected reproductive number is unbounded the outbreak size is proportional to agent population size and the temporal evolution is slower than exponential. The proposed framework can be used to model epidemic outbreaks using both empirical data obtained from previous outbreaks or by characterizing the contact process responsible for the disease transmission.