A twelve-month projection to September 2022 of the Covid-19 epidemic in the UK using a Dynamic Causal Model (preprint)

Objectives Predicting the future UK Covid-19 epidemic allows other countries to compare their epidemic with one unfolding without public health measures except a vaccine programme. Methods A Dynamic Causal Model (DCM) is used to estimate the model parameters of the epidemic such as vaccine effectiveness and increased transmissibility of alpha and delta variants, the vaccine programme roll-out and changes in contact rates. The model predicts the future trends in infections, long-Covid, hospital admissions and deaths. Results Two dose vaccination given to 66% of the UK population prevents transmission following infection by 44%, serious illness by 86% and death by 93%. Despite this, with no other public health measures used, cases will increase from 37 million to 61 million, hospital admission from 536,000 to 684,000 and deaths from 136,000 to 142,000 over twelve months. Discussion Vaccination alone will not control the epidemic. Relaxation of mitigating public health measures carries several risks including overwhelming the health services, the creation of vaccine resistant variants and the economic cost of huge numbers of acute and chronic cases.

Viral mutation, contact rates and testing: a DCM study of fluctuations (preprint)

This report considers three mechanisms that might underlie the course of the secondary peak of coronavirus infections in the United Kingdom. It considers: (i) fluctuations in transmission strength; (ii) seasonal fluctuations in contact rates and (iii) fluctuations in testing. Using dynamic causal modelling, we evaluated the contribution of all combinations of these three mechanisms using Bayesian model comparison. We found overwhelming evidence for the combination of all mechanisms, when explaining 16 types of data. Quantitatively, there was clear evidence for an increase in transmission strength of 57% over the past months (e.g., due to viral mutation), in the context of increased contact rates (e.g., rebound from national lockdowns) and increased test rates (e.g., due to the inclusion of lateral flow tests). Models with fluctuating transmission strength outperformed models with fluctuating contact rates. However, the best model included all three mechanisms suggesting that the resurgence during the second peak can be explained by an increase in effective contact rate that is the product of a rebound of contact rates following a national lockdown and increased transmission risk due to viral mutation.

Revealing the Transmission Dynamics of COVID-19: A Bayesian Framework for Rt Estimation (preprint)

In epidemiological modelling, the instantaneous reproduction number, Rt, is important to understand the transmission dynamics of infectious diseases. Current Rt estimates often suffer from problems such as lagging, averaging and uncertainties demoting the usefulness of Rt. To address these problems, we propose a new method in the framework of sequential Bayesian inference where a Data Assimilation approach is taken for Rt estimation, resulting in the state-of-the-art ‘DARt’ system for Rt estimation. With DARt, the problem of time misalignment caused by lagging observations is tackled by incorporating observation delays into the joint inference of infections and Rt; the drawback of averaging is improved by instantaneous updating upon new observations and a model selection mechanism capturing abrupt changes caused by interventions; the uncertainty is quantified and reduced by employing Bayesian smoothing. We validate the performance of DARt through simulations and demonstrate its power in revealing the transmission dynamics of COVID-19.

Dark matter, second waves and epidemiological modelling (preprint)

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.

Modelling lockdown-induced 2nd COVID waves in France (preprint)

As with the Spanish Flu a century ago, authorities have responded to the current COVID-19 pandemic with extraordinary public health measures. In particular, lockdown and related social distancing policies are motivated in some countries by the need to slow virus propagation - so that the primary wave of patients suffering from severe forms of COVID infection do not exceed the capacity of intensive care units. But unlocking poses a critical issue because relaxing social distancing may, in principle, generate secondary waves. Ironically however, the dynamic repertoire of established epidemiological models that support this kind of reasoning is limited to single epidemic outbreaks. In turn, predictions regarding secondary waves are tautologically derived from imposing assumptions about changes in the so-called "effective reproduction number". In this work, we depart from this approach and extend the LIST (Location-Infection-Symptom-Testing) model of the COVID pandemic with realistic nonlinear feedback mechanisms that under certain conditions, cause lockdown-induced secondary outbreaks. The original LIST model captures adaptive social distancing, i.e. the transient reduction of the number of person-to-person contacts (and hence the rate of virus transmission), as a societal response to salient public health risks. Here, we consider the possibility that such pruning of socio-geographical networks may also temporarily isolate subsets of local populations from the virus. Crucially however, such unreachable people will become susceptible again when adaptive social distancing relaxes and the density of contacts within socio-geographical networks increases again. Taken together, adaptive social distancing and network unreachability thus close a nonlinear feedback loop that endows the LIST model with a mechanism that can generate autonomous (lockdown-induced) secondary waves. However, whether and how secondary waves arise depend upon the interaction with other nonlinear mechanisms that capture other forms of transmission heterogeneity. We apply the ensuing LIST model to numerical simulations and exhaustive analyses of regional French epidemiological data. We find evidence for this kind of nonlinear feedback mechanism in the empirical dynamics of the pandemic in France. However, rather than generating catastrophic secondary outbreaks (as is typically assumed), the model predicts that the impact of lockdown-induced variations in population susceptibility and transmission may eventually reduce to a steady-state endemic equilibrium with a low but stable infection rate. In brief, except if immunity is lost (because of, e.g., virus mutations), a secondary COVID wave before winter is unlikely.

On the reliability of model-based predictions in the context of the current COVID epidemic event: impact of outbreak peak phase and data paucity (preprint)

The pandemic spread of the COVID-19 virus has, as of 20th of April 2020, reached most countries of the world. In an effort to design informed public health policies, many modelling studies have been performed to predict crucial outcomes of interest, including ICU solicitation, cumulated death counts, etc... The corresponding data analyses however, mostly rely on restricted (openly available) data sources, which typically include daily death rates and confirmed COVID cases time series. In addition, many of these predictions are derived before the peak of the outbreak has been observed yet (as is still currently the case for many countries). In this work, we show that peak phase and data paucity have a substantial impact on the reliability of model predictions. Although we focus on a recent model of the COVID pandemics, our conclusions most likely apply to most existing models, which are variants of the so-called 'Susceptible-Infected-Removed' or SIR framework. Our results highlight the need for performing systematic reliability evaluations for all models that currently inform public health policies. They also motivate a plea for gathering and opening richer and more reliable data time series (e.g., ICU occupancy, negative test rates, social distancing commitment reports, etc).

Estimating required lockdown cycles before immunity to SARS-CoV-2: Model-based analyses of susceptible population sizes, S0, in seven European countries including the UK and Ireland (preprint)

BackgroundFollowing stringent social distancing measures, some European countries are beginning to report a slowed or negative rate of growth of daily case numbers testing positive for the novel coronavirus. The notion that the first wave of infection is close to its peak begs the question of whether future peaks or second waves are likely. We sought to determine the current size of the effective (i.e. susceptible) population for seven European countries--to estimate immunity levels following this first wave. We compare these numbers to the total population sizes of these countries, in order to investigate the potential for future peaks. MethodsWe used Bayesian model inversion to estimate epidemic parameters from the reported case and death rates from seven countries using data from late January 2020 to April 5th 2020. Two distinct generative model types were employed: first a continuous time dynamical-systems implementation of a Susceptible-Exposed-Infectious-Recovered (SEIR) model and second: a partially observable Markov Decision Process (MDP) or hidden Markov model (HMM) implementation of an SEIR model. Both models parameterise the size of the initial susceptible population ( S0), as well as epidemic parameters. Parameter estimation ( data fitting) was performed using a standard Bayesian scheme (variational Laplace) designed to allow for latent unobservable states and uncertainty in model parameters. ResultsBoth models recapitulated the dynamics of transmissions and disease as given by case and death rates. The peaks of the current waves were predicted to be in the past for four countries (Italy, Spain, Germany and Switzerland) and to emerge in 0.5 - 2 weeks in Ireland and 1-3 weeks in the UK. For France one model estimated the peak within the past week and the other in the future in two weeks. Crucially, Maximum a posteriori (MAP) estimates of S0 for each country indicated effective population sizes of below 20% (of total population size), under both the continuous time and HMM models. Using for all countries--with a Bayesian weighted average across all seven countries and both models, we estimated that 6.4% of the total population would be immune. From the two models the maximum percentage of the effective population was estimated at 19.6% of the total population for the UK, 16.7% for Ireland, 11.4% for Italy, 12.8% for Spain, 18.8% for France, 4.7% for Germany and 12.9% for Switzerland. ConclusionOur results indicate that after the current wave, a large proportion of the total population will remain without immunity. This suggests that in the absence of strong seasonal effects, new medications or more comprehensive contact tracing, a further set of epidemic waves in different geographic centres are likely. These findings may have implications for exit strategies from any lockdown stage.