BeyondR₀: heterogeneity in secondary infections and probabilistic epidemic forecasting

Abstract

The basic reproductive number, R 0 , is one of the most common and most commonly misapplied numbers in public health. Often used to compare outbreaks and forecast pandemic risk, this single number belies the complexity that different epidemics can exhibit, even when they have the same R 0 . Here, we reformulate and extend a classic result from random network theory to forecast the size of an epidemic using estimates of the distribution of secondary infections, leveraging both its average R 0 and the underlying heterogeneity. Importantly, epidemics with lower R 0 can be larger if they spread more homogeneously (and are therefore more robust to stochastic fluctuations). We illustrate the potential of this approach using different real epidemics with known estimates for R 0 , heterogeneity and epidemic size in the absence of significant intervention. Further, we discuss the different ways in which this framework can be implemented in the data-scarce reality of emerging pathogens. Lastly, we demonstrate that without data on the heterogeneity in secondary infections for emerging infectious diseases like COVID-19 the uncertainty in outbreak size ranges dramatically. Taken together, our work highlights the critical need for contact tracing during emerging infectious disease outbreaks and the need to look beyond R 0 .

The effectiveness of backward contact tracing in networks

“…spreading 30 , and large variance in an individual's reproductive number 12 , as well as the final outbreak size 31 .…”

Superspreading events in the transmission dynamics of SARS-CoV-2: Opportunities for interventions and control

“…While Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) has moved swiftly around the globe, causing millions of Coronavirus Disease 2019 (COVID-19) cases, much attention has been given to the basic reproduction number (R 0 ), estimated to be roughly between 1.5 and 4 [ 1 ]. As the virus spread, it has become clear that relying on a single value to characterize the number of secondary infections—and thus estimates of the transmissibility of this virus—is inadequate to capture the true transmission dynamics and subsequent risk to humanity [ 2 ]. Indeed, a litany of official reports and anecdotes have identified key superspreading events (SSEs), which have propelled transmission and infected many.…”

Incorporating Social Determinants of Health into Modelling of COVID-19 and other Infectious Diseases: A Baseline Socio-economic Compartmental Model

“…all bear directly on and ; and could also be incorporated into a social compartmental model. Furthermore, as heterogeneity in transmission as a result of SD may also make superspreading events more likely in particular communities, the study of social inequalities while incorporating network effects across social groups along the lines of Chang et al (2021) and Hébert-Dufresne et al (2021) is a particularly interesting research avenue within this theme.…”

“…Furthermore, given the high economic costs of NPIs, an improvement of SIs will also have economic benefits. Again here, there might also be indirect network effects which may or may not influence the reproduction number ( Hébert-Dufresne et al, 2021 ).…”

“…We should highlight at this point that the linear form of equations (5) , (6) is a reasonable assumption given the focus of the paper on inequalities across countries. However, if the focus would have been within country inequalities, it would have been important to also allow for network effects related to heterogeneity in transmission (for example see Chang et al, 2021 , Hébert-Dufresne et al, 2021 ) which may also make superspreading events more likely in particular communities.…”