Estimation of heterogeneous instantaneous reproduction numbers with application to characterize SARS-CoV-2 transmission in Massachusetts counties
Authors: Zhou Zhenwei , Kolaczyk Eric , Thompson Robin , White Laura 
Published: December 2021

The reproductive number is an important metric that has been widely used to quantify the infectiousness of communicable diseases. The time-varying instantaneous reproductive number is useful for monitoring the real time dynamics of a disease to inform policy making for disease control. Local estimation of this metric, for instance at a county or city level, allows for more targeted interventions to curb transmission. However, simultaneous estimation of local reproductive numbers must account for potential sources of heterogeneity in these time-varying quantities – a key element of which is human mobility. We develop a statistical method that incorporates human mobility between multiple regions for estimating region-specific instantaneous reproductive numbers. The model also can account for exogenous cases imported from outside of the regions of interest. We propose two approaches to estimate the reproductive numbers, with mobility data used to adjust incidence in the first approach and to inform a formal priori distribution in the second (Bayesian) approach. Through a simulation study, we show that region-specific reproductive numbers can be well estimated if human mobility is reasonably well approximated by available data. We use this approach to estimate the instantaneous reproductive numbers of COVID-19 for 14 counties in Massachusetts using CDC case report data and the human mobility data collected by SafeGraph. We found that, accounting for mobility, our method produces estimates of reproductive numbers that are distinct across counties. In contrast, independent estimation of county-level reproductive numbers tends to produce similar values, as trends in county case-counts for the state are fairly concordant. These approaches can also be used to estimate any heterogeneity in transmission, for instance, age-dependent instantaneous reproductive number estimates. As people are more mobile and interact frequently in ways that permit transmission, it is important to account for this in the estimation of the reproductive number.

Author summary

To control the spreading of an infectious disease, it is very important to understand the real-time infectiousness of the pathogen that causes the disease. An existing metric called instantaneous reproductive number is often used to quantify the average number of secondary cases generated by individuals who are infectious at a certain time point, assuming no changes to current conditions. In practice, we might be interested in using the metric to describe the infectiousness in multiple regions. However, this is challenging when there are visitors traveling between these regions, since this could lead to a misclassification of where an individual is actually infected and create biased estimates for the instantaneous reproductive numbers. We developed a method that takes account of human mobility to estimate the instantaneous reproductive numbers for multiple regions simultaneously, which could reveal the heterogeneity of the metric. This method aims to provide helpful information on region-specific infectiousness for disease control measures that focus on the region with higher pathogen infectiousness. This approach is also applicable for estimating the reproductive number in the presence of other sources of heterogeneity, including by age.