‘Dark matter’, second waves and epidemiological modelling
Authors: Friston Karl J. , Costello Anthony , Pillay Deenan 
Published: September 2020

Background

Recent reports based on conventional SEIR models suggest that the next wave of the COVID-19 pandemic in the UK could overwhelm health services, with fatalities that far exceed the first wave. These models suggest non-pharmaceutical interventions would have limited impact without intermittent national lockdowns and consequent economic and health impacts. We used Bayesian model comparison to revisit these conclusions, when allowing for heterogeneity of exposure, susceptibility, and viral transmission.

Methods

We used dynamic causal modelling to estimate the parameters of epidemiological models and, crucially, the evidence for alternative models of the same data. We compared SEIR models of immune status that were equipped with latent factors generating data; namely, location, symptom, and testing status. We analysed daily cases and deaths from the US, UK, Brazil, Italy, France, Spain, Mexico, Belgium, Germany, and Canada over the period 25-Jan-20 to 15-Jun-20. These data were used to estimate the composition of each country’s population in terms of the proportions of people (i) not exposed to the virus, (ii) not susceptible to infection when exposed, and (iii) not infectious when susceptible to infection.

Findings

Bayesian model comparison found overwhelming evidence for heterogeneity of exposure, susceptibility, and transmission. Furthermore, both lockdown and the build-up of population immunity contributed to viral transmission in all but one country. Small variations in heterogeneity were sufficient to explain the large differences in mortality rates across countries. The best model of UK data predicts a second surge of fatalities will be much less than the first peak (31 vs. 998 deaths per day. 95% CI: 24-37)—substantially less than conventional model predictions. The size of the second wave depends sensitively upon the loss of immunity and the efficacy of find-test-trace-isolate-support (FTTIS) programmes.

Interpretation

A dynamic causal model that incorporates heterogeneity of exposure, susceptibility and transmission suggests that the next wave of the SARS-CoV-2 pandemic will be much smaller than conventional models predict, with less economic and health disruption. This heterogeneity means that seroprevalence underestimates effective herd immunity and, crucially, the potential of public health programmes.

Research in context

Evidence before this study

Hundreds of modelling papers have been published recently, offering predictions and projections of the current coronavirus outbreak. These range from peer-reviewed publications to rapid reports from learned societies. Many, if not most, of these modelling initiatives commit to a particular kind of epidemiological model that precludes heterogeneity in viral exposure, susceptibility, and transmission. The ensuing projections can be fantastical in terms of fatalities and ensuing public health responses.

Added value of this study

This study revisits the evidence for conventional epidemiological modelling assumptions using dynamic causal modelling and Bayesian model comparison. It provides overwhelming evidence for heterogeneity, and the interaction between lockdown and herd immunity in suppressing viral transmission.

Implications of all the available evidence

Heterogeneity of this sort means that low seroprevalence (<20%) is consistent with levels of population immunity that play a substantive role in attenuating viral transmission and, crucially, facilitating public health measures.