Dynamic causal modelling of COVID-19 and its mitigations

This technical report describes the dynamic causal modelling of mitigated epidemiological outcomes during the COVID-9 coronavirus outbreak in 2020. Dynamic causal modelling is a form of complex system modelling, which uses 'real world' timeseries to estimate the parameters of an underlying state space model using variational Bayesian procedures. Its key contribution-in an epidemiological setting-is to embed conventional models within a larger model of sociobehavioural responses-in a way that allows for (relatively assumption-free) forecasting. One advantage of using variational Bayes is that one can progressively optimise the model via Bayesian model selection: generally, the most likely models become more expressive as more data becomes available. This report summarises the model (on 6-Nov-20), eight months after the inception of dynamic causal modelling for COVID-19. This model-and its subsequent updates-is used to provide nowcasts and forecasts of latent behavioural and epidemiological variables as an open science resource. The current report describes the underlying model structure and the rationale for the variational procedures that underwrite Bayesian model selection

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

We recently described a dynamic causal model of a COVID-19 outbreak within a single region. Here, we combine several of these (epidemic) models 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.Comment: Technical report: 35 pages, 14 figures, 1 tabl

Well dispersed fractal aggregates as filler in polymer-silica nanocomposites: long range effects in rheology

We are presenting a new method of processing polystyrene-silica nanocomposites, which results in a very well-defined dispersion of small primary aggregates (assembly of 15 nanoparticles of 10 nm diameter) in the matrix. The process is based on a high boiling point solvent, in which the nanoparticles are well dispersed, and controlled evaporation. The filler's fine network structure is determined over a wide range of sizes, using a combination of Small Angle Neutron Scattering (SANS) and Transmission Electronic Microscopy (TEM). The mechanical response of the nanocomposite material is investigated both for small (ARES oscillatory shear and Dynamical Mechanical Analysis) and large deformations (uniaxial traction), as a function of the concentration of the particles. We can investigate the structure-property correlations for the two main reinforcement effects: the filler network contribution, and a filler-polymer matrix effect. Above a silica volume fraction threshold, we see a divergence of the modulus correlated to the build up of a connected network. Below the threshold, we obtain a new additional elastic contribution of much longer terminal time than the matrix. Since aggregates are separated by at least 60 nm, this new filler-matrix contribution cannot be described solely with the concept of glassy layer (2nm)

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.Comment: 20 pages, 8 figures, 3 tables (technical report

Second waves, social distancing, and the spread of COVID-19 across the USA [version 2; peer review: 2 approved with reservations]

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