Dynamic causal modelling of immune heterogeneity.

An interesting inference drawn by some COVID-19 epidemiological models is that there exists a proportion of the population who are not susceptible to infection-even at the start of the current pandemic. This paper introduces a model of the immune response to a virus. This is based upon the same sort of mean-field dynamics as used in epidemiology. However, in place of the location, clinical status, and other attributes of people in an epidemiological model, we consider the state of a virus, B and T-lymphocytes, and the antibodies they generate. Our aim is to formalise some key hypotheses as to the mechanism of resistance. We present a series of simple simulations illustrating changes to the dynamics of the immune response under these hypotheses. These include attenuated viral cell entry, pre-existing cross-reactive humoral (antibody-mediated) immunity, and enhanced T-cell dependent immunity. Finally, we illustrate the potential application of this sort of model by illustrating variational inversion (using simulated data) of this model to illustrate its use in testing hypotheses. In principle, this furnishes a fast and efficient immunological assay-based on sequential serology-that provides a (1) quantitative measure of latent immunological responses and (2) a Bayes optimal classification of the different kinds of immunological response (c.f., glucose tolerance tests used to test for insulin resistance). This may be especially useful in assessing SARS-CoV-2 vaccines.

Second waves, social distancing, and the spread of COVID-19 across the USA.

We recently described a dynamic causal model of a COVID-19 outbreak within a single region. Here, we combine several instantiations of this (epidemic) model to create a (pandemic) model of viral spread among regions. Our focus is on a second wave of new cases that may result from loss of immunity-and the exchange of people between regions-and how mortality rates can be ameliorated under different strategic responses. In particular, we consider hard or soft social distancing strategies predicated on national (Federal) or regional (State) estimates of the prevalence of infection in the population. The modelling is demonstrated using timeseries of new cases and deaths from the United States to estimate the parameters of a factorial (compartmental) epidemiological model of each State and, crucially, coupling between States. Using Bayesian model reduction, we identify the effective connectivity between States that best explains the initial phases of the outbreak in the United States. Using the ensuing posterior parameter estimates, we then evaluate the likely outcomes of different policies in terms of mortality, working days lost due to lockdown and demands upon critical care. The provisional results of this modelling suggest that social distancing and loss of immunity are the two key factors that underwrite a return to endemic equilibrium.

Effective immunity and second waves: a dynamic causal modelling study.

This technical report addresses a pressing issue in the trajectory of the coronavirus outbreak; namely, the rate at which effective immunity is lost following the first wave of the pandemic. This is a crucial epidemiological parameter that speaks to both the consequences of relaxing lockdown and the propensity for a second wave of infections. Using a dynamic causal model of reported cases and deaths from multiple countries, we evaluated the evidence models of progressively longer periods of immunity. The results speak to an effective population immunity of about three months that, under the model, defers any second wave for approximately six months in most countries. This may have implications for the window of opportunity for tracking and tracing, as well as for developing vaccination programmes, and other therapeutic interventions.

Dynamic causal modelling of COVID-19.

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 per se 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.

Effective immunity and second waves: a dynamic causal modelling study [version 1;peer review: awaiting peer review]

This technical report addresses a pressing issue in the trajectory of the coronavirus outbreak;namely, the rate at which effective immunity is lost following the first wave of the pandemic. This is a crucial epidemiological parameter that speaks to both the consequences of relaxing lockdown and the propensity for a second wave of infections. Using a dynamic causal model of reported cases and deaths from multiple countries, we evaluated the evidence models of progressively longer periods of immunity. The results speak to an effective population immunity of about three months that, under the model, defers any second wave for approximately six months in most countries. This may have implications for the window of opportunity for tracking and tracing, as well as for developing vaccination programmes, and other therapeutic interventions.