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.

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Effective immunity and second waves: a dynamic causal modelling study

Wellcome Open Research ◽

10.12688/wellcomeopenres.16253.2 ◽

2020 ◽

Vol 5 ◽

pp. 204

Author(s):

Karl J. Friston ◽

Thomas Parr ◽

Peter Zeidman ◽

Adeel Razi ◽

Guillaume Flandin ◽

...

Keyword(s):

Causal Model ◽

Therapeutic Interventions ◽

Window Of Opportunity ◽

Effective Population ◽

Causal Modelling ◽

Population Immunity ◽

Technical Report ◽

Dynamic Causal Model ◽

Second Wave ◽

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.

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Dark matter, second waves and epidemiological modelling

10.1101/2020.09.01.20185876 ◽

2020 ◽

Cited By ~ 2

Author(s):

Karl Friston ◽

Anthony Costello ◽

Deenan Pillay

Keyword(s):

Bayesian Model ◽

Model Comparison ◽

Herd Immunity ◽

Viral Transmission ◽

Population Immunity ◽

Bayesian Model Comparison ◽

Overwhelming Evidence ◽

Conventional Models ◽

The Uk ◽

Dynamic Causal Model

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.

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Effective immunity and second waves: a dynamic causal modelling study

Wellcome Open Research ◽

10.12688/wellcomeopenres.16253.1 ◽

2020 ◽

Vol 5 ◽

pp. 204

Author(s):

Karl J. Friston ◽

Thomas Parr ◽

Peter Zeidman ◽

Adeel Razi ◽

Guillaume Flandin ◽

...

Keyword(s):

Causal Model ◽

Therapeutic Interventions ◽

Window Of Opportunity ◽

Effective Population ◽

Causal Modelling ◽

Population Immunity ◽

Technical Report ◽

Dynamic Causal Model ◽

Second Wave ◽

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.

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How vaccination and contact isolation might interact to suppress transmission of Covid-19: a DCM study

10.1101/2021.01.03.20248972 ◽

2021 ◽

Author(s):

Karl J. Friston ◽

Anthony Costello ◽

Guillaume Flandin ◽

Adeel Razi

Keyword(s):

Causal Model ◽

Herd Immunity ◽

Contact Tracing ◽

Effective Vaccine ◽

Full Potential ◽

Contact Rates ◽

The United Kingdom ◽

Contact Isolation ◽

Community Transmission ◽

Dynamic Causal Model

AbstractThis report describes a dynamic causal model that could be used to address questions about the rollout and efficacy of vaccines in the United Kingdom. For example, is suppression of community transmission a realistic aspiration? And, if not, what kind of endemic equilibrium might be achieved? What percentage of the population needs to be vaccinated? And over what timescale? It focuses on the synergies among (i) vaccination, (ii) the supported isolation of contacts of confirmed cases and (iii) restrictions on contact rates (i.e., lockdown and social distancing). To model these mitigations, we used a dynamic causal model that embeds an epidemiological model into agent-based behavioural model. The model structure and parameters were optimised to best explain responses—to the first and subsequent waves—enabling predictions over the forthcoming year under counterfactual scenarios. Illustrative analyses suggest that the full potential of vaccination is realised by increasing the efficacy of contact tracing: for example, under idealised (best case) assumptions—of an effective vaccine and efficient isolation of infected pre-symptomatic cases— suppression of community transmission would require 50% herd immunity by vaccinating 22% by the end of 2021; i.e., 15 million people or about 50,000 per day. With no change in the isolation of contacts, 36% would require vaccination, i.e., 25 million people. These figures should not be read as estimates of the actual number of people requiring vaccination; however, they illustrate the potential of this kind of model to quantify interactions among public health interventions. We anticipate using this model in a few months—to estimate the average effectiveness of vaccines when more data become available.

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The Spirit of Cromwell’s Rule

10.1093/oso/9780198746904.003.0015 ◽

2018 ◽

Author(s):

Timothy McGrew

Keyword(s):

Bayesian Methods ◽

Bayesian Model ◽

Bayesian Probability ◽

Standard Textbook ◽

Per Se

One of the central complaints about Bayesian probability is that it places no constraints on individual subjectivity in one’s initial probability assignments. Those sympathetic to Bayesian methods have responded by adding restrictions motivated by broader epistemic concerns about the possibility of changing one’s mind. This chapter explores some cases where, intuitively, a straightforward Bayesian model yields unreasonable results. Problems arise in these cases not because there is something wrong with the Bayesian formalism per se but because standard textbook illustrations teach us to represent our inferences in simplified ways that break down in extreme cases. It also explores some interesting limitations on the extent to which successive items of evidence ought to induce us to change our minds when certain screening conditions obtain.

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Two decades after Korpi and Palme’s “paradox of redistribution”: What have we learned so far and where do we take it from here?

Journal of International and Comparative Social Policy ◽

10.1017/ics.2020.24 ◽

2021 ◽

pp. 1-16 ◽

Cited By ~ 1

Author(s):

Dimitri Gugushvili ◽

Tijs Laenen

Keyword(s):

Social Policy ◽

Income Inequality ◽

Critical Review ◽

Institutional Design ◽

State Of The Art ◽

Causal Chain ◽

Empirical Literature ◽

The Poor ◽

History Of ◽

Per Se

Abstract Over two decades ago, Korpi and Palme (1998) published one of the most influential papers in the history of social policy discipline, in which they put forward a “paradox of redistribution”: the more countries target welfare resources exclusively at the poor, the less redistribution is actually achieved and the less income inequality and poverty are reduced. The current paper provides a state-of-the-art review of empirical research into that paradox. More specifically, we break down the paradox into seven core assumptions, which together form a causal chain running from institutional design to redistributive outcomes. For each causal assumption, we offer a comprehensive and critical review of the relevant empirical literature, also including a broader range of studies that do not aim to address Korpi and Palme’s paradox per se, but are nevertheless informative about it.

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