Outbreak of Infectious Diseases through the Weighted Random Connection Model

Bell Labs, Alcatel-Lucent, 600 Mountain Avenue 2C-318, Murray Hill, NJ 07974, USA

^⋆ Corresponding author. E-mail: milan@research.bell-labs.com.

Abstract

When modeling the spread of infectious diseases, it is important to incorporate risk behavior of individuals in a considered population. Not only risk behavior, but also the network structure created by the relationships among these individuals as well as the dynamical rules that convey the spread of the disease are the key elements in predicting and better understanding the spread. In this work we propose the weighted random connection model, where each individual of the population is characterized by two parameters: its position and risk behavior. A goal is to model the effect that the probability of transmissions among individuals increases in the individual risk factors, and decays in their Euclidean distance. Moreover, the model incorporates a combined risk behavior function for every pair of the individuals, through which the spread can be directly modeled or controlled. We derive conditions for the existence of an outbreak of infectious diseases in this model. Our main result is the almost sure existence of an infinite component in the weighted random connection model. We use results on the random connection model and site percolation in Z².