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Probability and Combinatorics

Tuesday, May 2, 2017 - 3:00pm

Milan Bradonjic



University of Pennsylvania


When modeling the spread of infectious diseases, it is important toincorporate risk behavior of individuals in a considered population.Not only risk behavior, but also the network structure created by therelationships among these individuals as well as the dynamical rulesthat convey the spread of the disease are the key elements inpredicting and better understanding the spread. We propose theweighted random connection model, where each individual of thepopulation is characterized by two parameters: its position and riskbehavior. A goal is to model the effect that the probability oftransmissions among individuals increases in the individual riskfactors, and decays in their Euclidean distance. Moreover, the modelincorporates a combined risk behavior function for every pair of theindividuals, through which the spread can be directly modeled orcontrolled. The main results are conditions for the almost sureexistence of an infinite cluster in the weighted random connectionmodel. We use results on the random connection model and sitepercolation in Z^2.