Functional Central Limit Theorem for Susceptible-Infected Process on Configuration Model Graphs

• Activity Number: 520 - SPEED: Infectious Diseases, Spatial Modeling and Environmental Exposures, Speed 2
• Type: Contributed
• Date/Time: Wednesday, July 31, 2019 : 10:30 AM to 11:15 AM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Wasiur R. KhudaBukhsh* and Casper Woroszylo and Grzegorz A. Rempa?a and Heinz Koeppl
• Companies: Ohio State University and BHP Billiton and Ohio State University and TU Darmstadt
• Keywords: SI process; Functional CLT; Configuration model; percolation; epidemic process on networks

Abstract

We study a stochastic compartmental susceptible-infected (SI) epidemic process on a configuration model random graph with a given degree distribution over a finite time interval. We split the population of graph nodes into two compartments, namely, S and I, denoting susceptible and infected nodes, respectively. In addition to the sizes of these two compartments, we study counts of SI-edges (those connecting a susceptible and an infected node), and SS-edges (those connecting two susceptible nodes). We describe the dynamical process in terms of these counts and present a functional central limit theorem (FCLT) for them when the number of nodes in the random graph grows to infinity. To be precise, we show that these counts, when appropriately scaled, converge weakly to a continuous Gaussian vector martingale process in the space of vector-valued càdlàg functions endowed with the Skorohod topology. (Joint work with Casper Woroszylo, Grzegorz A. Rempa?a, and Heinz Koeppl.)