Motivated by the need for novel robust approaches to modelling the COVID-19 pandemic, this talk will focus on a population of $N$ individuals viewed as an inhomogeneous random social network (IRSN). The nodes of the network represent different types of individuals (classified by attributes such as age, profession, location etc) and the edges represent significant social relationships. An epidemic is pictured as a contagion process that evolves daily, triggered on day $0$ by a seed infection introduced into the population. A simple agent-based model (ABM) is proposed that captures stylized features of the infection transmission process. Individuals' social behaviour and health status are assumed to be random, with probability distributions that vary with their type. First a formulation is given for the basic SI (``susceptible-infective'') network contagion model, which focusses on the cumulative number of people that have been infected. The main result is an analytical formula valid in the large $N$ limit of the ABM, for the state of the system on day $t$. The formula involves only one-dimensional integration that can be implemented efficiently using the fast Fourier transform. Next, more realistic ``edge-based SIR compartment models’', including ``removed'' (R) and ``exposed'' (E) classes, are formulated. These models also lead to analytical formulas that generalize the results for the SI network model. This talk will conclude with examples of how the IRSN framework can be easily adapted for analysis of different kinds of public health interventions, including vaccination, social distancing and quarantine.

Paper: https://arxiv.org/abs/2004.02779

Bio: Tom Hurd is a professor of mathematics who has worked extensively in mathematical physics and financial mathematics. He is currently a co-leader of the CQAM-Fields Systemic Risk Analytics Lab. His modelling project for COVID-19 was motivated by his 2016 book ``Contagion: Systemic Risk in Financial Networks’’ which explored cascade models on networks of complex financial institutions. The title suggested that his methods might provide a novel perspective into the current pandemic.