Multi-type branching and graph product theory of infectious disease outbreaks

Vazquez, A.

The heterogeneity of human populations is a major challenge to mathematical descriptions of infectious disease outbreaks. Numerical simulations are therefore deployed to account for the many factors influencing the disease spreading dynamics. Yet, the results from numerical simulations are often as complicated as the reality, leaving us with a sense of confusion about how the different factors account for the simulation results. Here, using a multi-type branching together with a graph tensor product approach, I derive a single equation for the effective reproductive number of an infectious disease outbreak. Using this equation I deconvolute the impact of crowd management, contact heterogeneity, testing, vaccination, mask use and smartphone tracing app use. This equation can be used to gain a basic understanding of infectious disease outbreaks and their simulations.