Abstract
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.
Highlights
We will see examples of this later. This aspect of dynamic causal modelling means that one does not have to commit to a particular form of a model
Does social distancing behaviour depend upon the number of people who are infected? Or, does it depend on how many people have tested positive for COVID-19?
One can use standard variational techniques (Friston et al, 2007) to estimate the posterior over model parameters and evaluate a variational bound on the model evidence or marginal likelihood
Summary
Pr(symptoms | infected) Pr(ARDS | symptomatic) symptomatic period (days) acute RDS period (days) Pr(fatality | CCU) Pr(survival | home). Any second wave can be treated as the first wave of another city or region Under this choice, the population size can be set, a priori, to 1,000,000; noting that a small city comprises (by definition) a hundred thousand people, while a large city can exceed 10 million. The population size can be set, a priori, to 1,000,000; noting that a small city comprises (by definition) a hundred thousand people, while a large city can exceed 10 million Note that this is a prior expectation, the effective population size is estimated from the data: the assumption that the effective population size reflects the total population of a country is a hypothesis (that we will test later). Because we are dealing with large populations, the likelihood of any observed daily count has a binomial distribution that can be approximated by a Gaussian density
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