Early epidemic spread, percolation and Covid-19

TL;DR

This paper models early epidemic spread using complex networks with multiple interaction types, extending percolation theory results, deriving an explicit $R_0$ formula, and applying it to Covid-19 data across different countries.

Contribution

It extends percolation-based epidemic models to multiple interaction types, providing an explicit $R_0$ formula and applying it to Covid-19 scenarios.

Findings

Explicit $R_0$ formula depending on interaction probabilities and degree moments.

Low probability of no-epidemic outcome without interventions.

Model applicability to Covid-19 transmission in various countries.

Abstract

Human to human transmissible infectious diseases spread in a population using human interactions as its transmission vector. The early stages of such an outbreak can be modeled by a graph whose edges encode these interactions between individuals, the vertices. This article attempts to account for the case when each individual entails in different kinds of interactions which have therefore different probabilities of transmitting the disease. The majority of these results can be also stated in the language of percolation theory. The main contributions of the article are: (1) Extend to this setting some results which were previously known in the case when each individual has only one kind of interactions. (2) Find an explicit formula for the basic reproduction number $R_0$ which depends only on the probabilities of transmitting the disease along the different edges and the first two moments of the degree distributions of the associated graphs. (3) Motivated by the recent Covid-19 pandemic, we use the framework developed to compute the $R_0$ of a model disease spreading in populations whose trees and degree distributions are adjusted to several different countries. In this setting, we shall also compute the probability that the outbreak will not lead to an epidemic. In all cases we find such probability to be very low if no interventions are put in place.