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 program. Methods A Dynamic Causal Model was used to estimate key model parameters of the UK epidemic, such as vaccine effectiveness and increased transmissibility of Alpha and Delta variants, the effectiveness of the vaccine program 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 admissions from 536,000 to 684,000 and deaths from 136,000 to 142,000 over 12 months. A retrospective analysis (conducted after the original submission of this report) allowed a comparison of these predictions of morbidity and mortality with actual outcomes. Conclusion Vaccination alone will not control the epidemic. Relaxation of mitigating public health measures carries several risks, which include overwhelming the health services, the creation of vaccine resistant variants and the economic cost of huge numbers of acute and chronic cases.
This article was written at the invitation of the Editor, in response to the preceding article by Strother et aI. (1995). I have taken this opportunity to comment on several issues, some of which have been the subject of recent exchanges (e.g. , Taylor et aI., 1993; Worsley et aI. , 1993). Others deserve mention because they have become of special cur rent interest. An overview of the development of statistical analysis in functional imaging is pre sented, followed by a discussion of some key areas.
This article considers the efficiency of event-related fMRI designs in terms of the optimum temporal pattern of stimulus or trial presentations. The distinction between “stochastic” and “deterministic” is used to distinguish between designs that are specified in terms of the probability that an event will occur at a series of time points (stochastic) and those in which events always occur at prespecified time (deterministic). Stochastic designs may be “stationary,” in which the probability is constant, or nonstationary, in which the probabilities change with time. All these designs can be parameterized in terms of a vector of occurrence probabilities and a prototypic design matrix that embodies constraints (such as the minimum stimulus onset asynchrony) and the model of hemodynamic responses. A simple function of these parameters is presented and used to compare the relative efficiency of different designs. Designs with slow modulation of occurrence probabilities are generally more efficient than stationary designs. Interestingly the most efficient design is a conventional block design. A critical point, made in this article, is that the most efficient design for one effect may not be the most efficient for another. This is particularly important when considering evoked responses and the differences among responses. The most efficient designs for evoked responses, as opposed to differential responses, require trial-free periods during which baseline levels can be attained. In the context of stochastic, rapid-presentation designs this is equivalent to the inclusion of “null events.”
In this article we used biologically plausible simulations of coupled neuronal populations to address the relationship between phasic and fast coherent neuronal interactions and macroscopic measures of activity that are integrated over time, such as the BOLD response in functional magnetic resonance imaging. Event-related, dynamic correlations were assessed using joint peristimulus time histograms and, in particular, the mutual information between stimulus-induced transients in two populations. This mutual information can be considered as an index of functional connectivity. Our simulations showed that functional connectivity or dynamic integration between two populations increases with mean background activity and stimulus-related rate modulation. Furthermore, as the background activity increases, the populations become increasingly sensitive to the intensity of the stimulus in terms of a predisposition to transient phase locking. This reflects an interaction between background activity and stimulus intensity in producing dynamic correlations, in that background activity augments stimulus-induced coherence modulation. This is interesting from a computational perspective because background activity establishes a context that may have a profound effect on event-related interactions or functional connectivity between neuronal populations. Finally, total firing rates, which subsume both background activity and stimulus-related rate modulation, were almost linearly related to the expression of dynamic correlations over large ranges of activities. These observations show that under the assumptions implicit in our model, rate-specific metrics based on rate or coherence modulation may be different perspectives on the same underlying dynamics. This suggests that activity (averaged over all peristimulus times), as measured in neuroimaging, may be tightly coupled to the expression of dynamic correlations.
<ns4:p>This technical report describes a dynamic causal model of the spread of coronavirus through a population. The model is based upon ensemble or population dynamics that generate outcomes, like new cases and deaths over time. The purpose of this model is to quantify the uncertainty that attends predictions of relevant outcomes. By assuming suitable conditional dependencies, one can model the effects of interventions (e.g., social distancing) and differences among populations (e.g., herd immunity) to predict what might happen in different circumstances. Technically, this model leverages state-of-the-art variational (Bayesian) model inversion and comparison procedures, originally developed to characterise the responses of neuronal ensembles to perturbations. Here, this modelling is applied to epidemiological populations—to illustrate the kind of inferences that are supported and how the model <ns4:italic>per se</ns4:italic> can be optimised given timeseries data. Although the purpose of this paper is to describe a modelling protocol, the results illustrate some interesting perspectives on the current pandemic; for example, the nonlinear effects of herd immunity that speak to a self-organised mitigation process.</ns4:p>