Network-augmented compartmental models to track asymptomatic disease spread

Abstract

A major challenge in understanding the spread of certain newly emerging viruses is the presence of asymptomatic cases. Their prevalence is hard to measure in the absence of testing tools, and yet the information is critical for tracking disease spread and shaping public health policies. Here, we introduce a framework that combines classic compartmental models with travel networks and we use it to estimate asymptomatic rates. Our platform, traSIR (“tracer”), is an augmented SIR (susceptible-infectious-recovered) model that incorporates multiple locations and the flow of people between them; it has a compartment model for each location and estimates of commuting traffic between compartments. TraSIR models both asymptomatic and symptomatic infections, as well as the dampening effect symptomatic infections have on traffic between locations. We derive analytical formulae to express the asymptomatic rate as a function of other key model parameters. Next, we use simulations to show that empirical data fitting yields excellent agreement with actual asymptomatic rates using only information about the number of symptomatic infections over time and compartments. Finally, we apply our model to COVID-19 data consisting of reported daily infections in the New York metropolitan area and estimate asymptomatic rates of COVID-19 to be ∼34%, which is within the 30%–40% interval derived from widespread testing. Overall, our work demonstrates that traSIR is a powerful approach to express viral propagation dynamics over geographical networks and estimate key parameters relevant to virus transmission.