Dynamic causal modelling of COVID-19

Climate change and disorders of the nervous system

Anthropogenic climate change is affecting people's health, including those with neurological and psychiatric diseases. Currently, making inferences about the effect of climate change on neurological and psychiatric diseases is challenging because of an overall sparsity of data, differing study methods, paucity of detail regarding disease subtypes, little consideration of the effect of individual and population genetics, and widely differing geographical locations with the potential for regional influences. However, evidence suggests that the incidence, prevalence, and severity of many nervous system conditions (eg, stroke, neurological infections, and some mental health disorders) can be affected by climate change. The data show broad and complex adverse effects, especially of temperature extremes to which people are unaccustomed and wide diurnal temperature fluctuations. Protective measures might be possible through local forecasting. Few studies project the future effects of climate change on brain health, hindering policy developments. Robust studies on the threats from changing climate for people who have, or are at risk of developing, disorders of the nervous system are urgently needed.

A primer on Variational Laplace (VL)

This article details a scheme for approximate Bayesian inference, which has underpinned thousands of neuroimaging studies since its introduction 15 years ago. Variational Laplace (VL) provides a generic approach to fitting linear or non-linear models, which may be static or dynamic, returning a posterior probability density over the model parameters and an approximation of log model evidence, which enables Bayesian model comparison. VL applies variational Bayesian inference in conjunction with quadratic or Laplace approximations of the evidence lower bound (free energy). Importantly, update equations do not need to be derived for each model under consideration, providing a general method for fitting a broad class of models. This primer is intended for experimenters and modellers who may wish to fit models to data using variational Bayesian methods, without assuming previous experience of variational Bayes or machine learning. Accompanying code demonstrates how to fit different kinds of model using the reference implementation of the VL scheme in the open-source Statistical Parametric Mapping (SPM) software package. In addition, we provide a standalone software function that does not require SPM, in order to ease translation to other fields, together with detailed pseudocode. Finally, the supplementary materials provide worked derivations of the key equations.

Inferring Trajectories of Psychotic Disorders Using Dynamic Causal Modeling

Introduction

Illness course plays a crucial role in delineating psychiatric disorders. However, existing nosologies consider only its most basic features (e.g., symptom sequence, duration). We developed a Dynamic Causal Model (DCM) that characterizes course patterns more fully using dense timeseries data. This foundational study introduces the new modeling approach and evaluates its validity using empirical and simulated data.

Methods

A three-level DCM was constructed to model how latent dynamics produce symptoms of depression, mania, and psychosis. This model was fit to symptom scores of nine patients collected prospectively over four years, following first hospitalization. Simulated subjects based on these empirical data were used to evaluate model parameters at the subject-level. At the group-level, we tested the accuracy with which the DCM can estimate the latent course patterns using Parametric Empirical Bayes (PEB) and leave-one-out cross-validation.

Results

Analyses of empirical data showed that DCM accurately captured symptom trajectories for all nine subjects. Simulation results showed that parameters could be estimated accurately (correlations between generative and estimated parameters >= 0.76). Moreover, the model could distinguish different latent course patterns, with PEB correctly assigning simulated patients for eight of nine course patterns. When testing any pair of two specific course patterns using leave-one-out cross-validation, 30 out of 36 pairs showed a moderate or high out-of-samples correlation between the true group-membership and the estimated group-membership values.

Conclusion

DCM has been widely used in neuroscience to infer latent neuronal processes from neuroimaging data. Our findings highlight the potential of adopting this methodology for modeling symptom trajectories to explicate nosologic entities, temporal patterns that define them, and facilitate personalized treatment.

Investigation of Factors Affecting COVID-19 and Sixth Wave Management Using a System Dynamics Approach

The COVID-19 pandemic has plunged the world into a health and economic crisis never seen before since the Spanish flu pandemic in 1918. The closure of schools and universities, the banning of rallies, and other social distancing in countries have been done to disrupt the transmission of the virus. Governments have planned to reduce restrictions on corona management by implementing vaccination programs. This research aims to better understand the Coronavirus disease's behavior, identify the prevalent factors, and adopt effective policies to control the pandemic. This study examines the different scenarios of releasing the constraints and returning to normal conditions before Corona to analyze the results of different scenarios to prevent the occurrence of subsequent peaks. The system dynamics approach is an effective means of studying COVID-19's behavioral characteristics. The factors that affect Coronavirus disease outbreak and control by expanding the basic SEIR model, interventions, and policies, such as vaccination, were investigated in this research. Based on the obtained results, the most critical factor in reducing the prevalence of the disease is reducing the behavioral risks of people and increasing the vaccination process. Observance of hygienic principles leads to disruption of the transmission chain, and vaccination increases the immunity of individuals against the acute type of infection. In addition, the closure of businesses and educational centers, along with government support for incomes, effectively controls and reduces the pandemic, which requires cooperation between the people and the government. In a situation where a new type of corona has spread, if the implementation of the policy of reducing restrictions and reopening schools and universities is done without planning, it will cause a lot of people to suffer.

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.

From Generative Models to Generative Passages: A Computational Approach to (Neuro) Phenomenology

This paper presents a version of neurophenomenology based on generative modelling techniques developed in computational neuroscience and biology. Our approach can be described as computational phenomenology because it applies methods originally developed in computational modelling to provide a formal model of the descriptions of lived experience in the phenomenological tradition of philosophy (e.g., the work of Edmund Husserl, Maurice Merleau-Ponty, etc.). The first section presents a brief review of the overall project to naturalize phenomenology. The second section presents and evaluates philosophical objections to that project and situates our version of computational phenomenology with respect to these projects. The third section reviews the generative modelling framework. The final section presents our approach in detail. We conclude by discussing how our approach differs from previous attempts to use generative modelling to help understand consciousness. In summary, we describe a version of computational phenomenology which uses generative modelling to construct a computational model of the inferential or interpretive processes that best explain this or that kind of lived experience.

The gut microbiome as a biomarker of differential susceptibility to SARS-CoV-2

Coronavirus disease 2019 (COVID-19) continues to exact a devastating global toll. Ascertaining the factors underlying differential susceptibility and prognosis following viral exposure is critical to improving public health responses. We propose that gut microbes may contribute to variation in COVID-19 outcomes. We synthesise evidence for gut microbial contributions to immunity and inflammation, and associations with demographic factors affecting disease severity. We suggest mechanisms potentially underlying microbially mediated differential susceptibility to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). These include gut microbiome-mediated priming of host inflammatory responses and regulation of endocrine signalling, with consequences for the cellular features exploited by SARS-CoV-2 virions. We argue that considering gut microbiome-mediated mechanisms may offer a lens for appreciating differential susceptibility to SARS-CoV-2, potentially contributing to clinical and epidemiological approaches to understanding and managing COVID-19.

Predicting and forecasting the impact of local outbreaks of COVID-19: use of SEIR-D quantitative epidemiological modelling for healthcare demand and capacity

BACKGROUND

The world is experiencing local/regional hotspots and spikes in the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which causes COVID-19 disease. We aimed to formulate an applicable epidemiological model to accurately predict and forecast the impact of local outbreaks of COVID-19 to guide the local healthcare demand and capacity, policy-making and public health decisions.

METHODS

The model utilized the aggregated daily COVID-19 situation reports (including counts of daily admissions, discharges and bed occupancy) from the local National Health Service (NHS) hospitals and COVID-19-related weekly deaths in hospitals and other settings in Sussex (population 1.7 million), Southeast England. These data sets corresponded to the first wave of COVID-19 infections from 24 March to 15 June 2020. A novel epidemiological predictive and forecasting model was then derived based on the local/regional surveillance data. Through a rigorous inverse parameter inference approach, the model parameters were estimated by fitting the model to the data in an optimal sense and then subsequent validation.

RESULTS

The inferred parameters were physically reasonable and matched up to the widely used parameter values derived from the national data sets by Biggerstaff M, Cowling BJ, Cucunubá ZM et al. (Early insights from statistical and mathematical modeling of key epidemiologic parameters of COVID-19, Emerging infectious diseases. 2020;26(11)). We validate the predictive power of our model by using a subset of the available data and comparing the model predictions for the next 10, 20 and 30 days. The model exhibits a high accuracy in the prediction, even when using only as few as 20 data points for the fitting.

CONCLUSIONS

We have demonstrated that by using local/regional data, our predictive and forecasting model can be utilized to guide the local healthcare demand and capacity, policy-making and public health decisions to mitigate the impact of COVID-19 on the local population. Understanding how future COVID-19 spikes/waves could possibly affect the regional populations empowers us to ensure the timely commissioning and organization of services. The flexibility of timings in the model, in combination with other early-warning systems, produces a time frame for these services to prepare and isolate capacity for likely and potential demand within regional hospitals. The model also allows local authorities to plan potential mortuary capacity and understand the burden on crematoria and burial services. The model algorithms have been integrated into a web-based multi-institutional toolkit, which can be used by NHS hospitals, local authorities and public health departments in other regions of the UK and elsewhere. The parameters, which are locally informed, form the basis of predicting and forecasting exercises accounting for different scenarios and impacts of COVID-19 transmission.

Causal Information Rate

Information processing is common in complex systems, and information geometric theory provides a useful tool to elucidate the characteristics of non-equilibrium processes, such as rare, extreme events, from the perspective of geometry. In particular, their time-evolutions can be viewed by the rate (information rate) at which new information is revealed (a new statistical state is accessed). In this paper, we extend this concept and develop a new information-geometric measure of causality by calculating the effect of one variable on the information rate of the other variable. We apply the proposed causal information rate to the Kramers equation and compare it with the entropy-based causality measure (information flow). Overall, the causal information rate is a sensitive method for identifying causal relations.

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.

Message Passing and Metabolism

Active inference is an increasingly prominent paradigm in theoretical biology. It frames the dynamics of living systems as if they were solving an inference problem. This rests upon their flow towards some (non-equilibrium) steady state-or equivalently, their maximisation of the Bayesian model evidence for an implicit probabilistic model. For many models, these self-evidencing dynamics manifest as messages passed among elements of a system. Such messages resemble synaptic communication at a neuronal network level but could also apply to other network structures. This paper attempts to apply the same formulation to biochemical networks. The chemical computation that occurs in regulation of metabolism relies upon sparse interactions between coupled reactions, where enzymes induce conditional dependencies between reactants. We will see that these reactions may be viewed as the movement of probability mass between alternative categorical states. When framed in this way, the master equations describing such systems can be reformulated in terms of their steady-state distribution. This distribution plays the role of a generative model, affording an inferential interpretation of the underlying biochemistry. Finally, we see that-in analogy with computational neurology and psychiatry-metabolic disorders may be characterized as false inference under aberrant prior beliefs.

Back to basics in COVID-19: Antigens and antibodies-Completing the puzzle

The outbreak of the coronavirus disease 2019 (COVID-19) has gathered 1 year of scientific/clinical information. This informational asset should be thoroughly and wisely used in the coming year colliding in a global task force to control this infection. Epidemiology of this infection shows that the available estimates of SARS-CoV-2 infection prevalence largely depended on the availability of molecular testing and the extent of tested population. Within molecular diagnosis, the viability and infectiousness of the virus in the tested samples should be further investigated. Moreover, SARS-CoV-2 has a genetic normal evolution that is a dynamic process. The immune system participates to the counterattack of the viral infection by pathogen elimination, cellular homoeostasis, tissue repair and generation of memory cells that would be reactivated upon a second encounter with the same virus. In all these stages, we still have knowledge to be gathered regarding antibody persistence, protective effects and immunological memory. Moreover, information regarding the intense pro-inflammatory action in severe cases still lacks and this is important in stratifying patients for difficult to treat cases. Without being exhaustive, the review will cover these important issues to be acknowledged to further advance in the battle against the current pandemia.

COVID-19: Short term prediction model using daily incidence data

Background

Prediction of the dynamics of new SARS-CoV-2 infections during the current COVID-19 pandemic is critical for public health planning of efficient health care allocation and monitoring the effects of policy interventions. We describe a new approach that forecasts the number of incident cases in the near future given past occurrences using only a small number of assumptions.

Methods

Our approach to forecasting future COVID-19 cases involves 1) modeling the observed incidence cases using a Poisson distribution for the daily incidence number, and a gamma distribution for the series interval; 2) estimating the effective reproduction number assuming its value stays constant during a short time interval; and 3) drawing future incidence cases from their posterior distributions, assuming that the current transmission rate will stay the same, or change by a certain degree.

Results

We apply our method to predicting the number of new COVID-19 cases in a single state in the U.S. and for a subset of counties within the state to demonstrate the utility of this method at varying scales of prediction. Our method produces reasonably accurate results when the effective reproduction number is distributed similarly in the future as in the past. Large deviations from the predicted results can imply that a change in policy or some other factors have occurred that have dramatically altered the disease transmission over time.

Conclusion

We presented a modelling approach that we believe can be easily adopted by others, and immediately useful for local or state planning.

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.

"Stay at Home, Protect the National Health Service, Save Lives": A cost benefit analysis of the lockdown in the United Kingdom

INTRODUCTION

The COVID-19 pandemic has transformed lives across the world. In the UK, a public health driven policy of population "lockdown" has had enormous personal and economic impact.

METHODS

We compare UK response and outcomes with European countries of similar income and healthcare resources. We calibrate estimates of the economic costs as different % loss in Gross Domestic Product (GDP) against possible benefits of avoiding life years lost, for different scenarios where current COVID-19 mortality and comorbidity rates were used to calculate the loss in life expectancy and adjusted for their levels of poor health and quality of life. We then apply a quality-adjusted life years (QALY) value of £30,000 (maximum under national guidelines).

RESULTS

There was a rapid spread of cases and significant variation both in severity and timing of both implementation and subsequent reductions in social restrictions. There was less variation in the trajectory of mortality rates and excess deaths, which have fallen across all countries during May/June 2020. The average age at death and life expectancy loss for non-COVID-19 was 79.1 and 11.4 years, respectively, while COVID-19 were 80.4 and 10.1 years; including adjustments for life-shortening comorbidities and quality of life plausibly reduces this to around 5 QALY lost for each COVID-19 death. The lowest estimate for lockdown costs incurred was 40% higher than highest benefits from avoiding the worst mortality case scenario at full life expectancy tariff and in more realistic estimations they were over 5 times higher. Future scenarios showed in the best case a QALY value of £220k (7xNICE guideline) and in the worst-case £3.7m (125xNICE guideline) was needed to justify the continuation of lockdown.

CONCLUSION

This suggests that the costs of continuing severe restrictions are so great relative to likely benefits in lives saved that a rapid easing in restrictions is now warranted.

Standard and Anomalous Waves of COVID-19: A Multiple-Wave Growth Model for Epidemics

We apply a generalized logistic growth model, with time-dependent parameters, to describe the fatality curves of the COVID-19 disease for several countries that exhibit multiple waves of infections. In the case of two waves only, the model parameters vary as a function of time according to a logistic function, whose two extreme values, i.e., for early and late times, characterize the first and second waves, respectively. For the multiple-wave model, the time-dependency of the parameters is likewise described by a multi-step logistic function with N intermediate plateaus, representing the N waves of the epidemic. We show that the theoretical curves are in excellent agreement with the empirical data for all countries considered here, namely: Brazil, Canada, Germany, Iran, Italy, Japan, Mexico, South Africa, Sweden, and the USA. The model also allows for predictions about the time of occurrence and severity of the subsequent waves. It is shown furthermore that the subsequent waves of COVID-19 can be generically classified into two main types, namely, standard and anomalous waves, according as to whether a given wave starts well after or well before the preceding one has subsided, respectively.

Conclusions

This chapter presents the usage of data science, which further helps in exploring the global pandemic COVID-19. This disease suppresses an overwhelming burden, not only to healthcare systems but to the world's economy too. In this era of techniques and technologies, it is believed that data science can better utilize scarce healthcare resources. In this chapter, we provide an introduction of data science and its applications, which helps in combating different aspects of COVID-19. Publicly available datasets related to disease are used as community resources. Different kinds of datasets are used to analyze various aspects of pandemic at different scales. These different kinds of datasets can be audio, video, textual, speech, and sensor data. More than hundreds of research articles are also studied to prepare a bibliometric study. Apart from grabbing all the advantages from datasets, this paper highlights a few challenges, such as surety of correct data, need of multidisciplinary collaboration, new data modality, security issues, and availability of data.

'Dark matter', second waves and epidemiological modelling

Recent reports using conventional Susceptible, Exposed, Infected and Removed models suggest that the next wave of the COVID-19 pandemic in the UK could overwhelm health services, with fatalities exceeding the first wave. We used Bayesian model comparison to revisit these conclusions, allowing for heterogeneity of exposure, susceptibility and transmission. We used dynamic causal modelling to estimate the evidence for alternative models of daily cases and deaths from the USA, the UK, Brazil, Italy, France, Spain, Mexico, Belgium, Germany and Canada over the period 25 January 2020 to 15 June 2020. These data were used to estimate 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. Bayesian model comparison furnished 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 large differences in mortality rates. The best model of UK data predicts a second surge of fatalities will be much less than the first peak. The size of the second wave depends sensitively on the loss of immunity and the efficacy of Find-Test-Trace-Isolate-Support programmes. In summary, accounting for 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.

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.

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.

On COVID-19 Modelling

This is an analysis of the COVID-19 pandemic by comparably simple mathematical and numerical methods. The final goal is to predict the peak of the epidemic outbreak per country with a reliable technique. The difference to other modelling approaches is to stay extremely close to the available data, using as few hypotheses and parameters as possible. For the convenience of readers, the basic notions of modelling epidemics are collected first, focusing on the standard SIR model. Proofs of various properties of the model are included. But such models are not directly compatible with available data. Therefore a special variation of a SIR model is presented that directly works with the data provided by the Johns Hopkins University. It allows to monitor the registered part of the pandemic, but is unable to deal with the hidden part. To reconstruct data for the unregistered Infected, a second model uses current experimental values of the infection fatality rate and a data-driven estimation of a specific form of the recovery rate. All other ingredients are data-driven as well. This model allows predictions of infection peaks. Various examples of predictions are provided for illustration. They show what countries have to face that are still expecting their infection peak. Running the model on earlier data shows how closely the predictions follow the transition from an uncontrolled outbreak to the mitigation situation by non-pharmaceutical interventions like contact restrictions.

Supplementary Information

The online version of this article (10.1365/s13291-020-00219-9) contains supplementary material, which is available to authorized users.

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.