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We consider a continuous-time Markov chain model of SIR disease dynamics with two levels of mixing. For this so-called stochastic households model, we provide two methods for inferring the model parameters---governing within-household transmission, recovery, and between-household transmission---from data of the day upon which each individual became infectious and the household in which each infection occurred, as would be available from first few hundred studies. Each method is a form of Bayesian Markov Chain Monte Carlo that allows us to calculate a joint posterior distribution for all parameters and hence the household reproduction number and the early growth rate of the epidemic. The first method performs exact Bayesian inference using a standard data-augmentation approach; the second performs approximate Bayesian inference based on a likelihood approximation derived from branching processes. These methods are compared for computational efficiency and posteriors from each are compared. The branching process is shown to be an excellent approximation and remains computationally efficient as the amount of data is increased.
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Knowing COVID-19 epidemiological distributions, such as the time from patient admission to death, is directly relevant to effective primary and secondary care planning, and moreover, the mathematical modelling of the pandemic generally. We determine epidemiological distributions for patients hospitalised with COVID-19 using a large dataset ($N=21{,}000-157{,}000$) from the Brazilian Sistema de Informac{c}~ao de Vigil^ancia Epidemiologica da Gripe database. A joint Bayesian subnational model with partial pooling is used to simultaneously describe the 26 states and one federal district of Brazil, and shows significant variation in the mean of the symptom-onset-to-death time, with ranges between 11.2-17.8 days across the different states, and a mean of 15.2 days for Brazil. We find strong evidence in favour of specific probability density function choices: for example, the gamma distribution gives the best fit for onset-to-death and the generalised log-normal for onset-to-hospital-admission. Our results show that epidemiological distributions have considerable geographical variation, and provide the first estimates of these distributions in a low and middle-income setting. At the subnational level, variation in COVID-19 outcome timings are found to be correlated with poverty, deprivation and segregation levels, and weaker correlation is observed for mean age, wealth and urbanicity.
In this work we demonstrate how to automate parts of the infectious disease-control policy-making process via performing inference in existing epidemiological models. The kind of inference tasks undertaken include computing the posterior distribution over controllable, via direct policy-making choices, simulation model parameters that give rise to acceptable disease progression outcomes. Among other things, we illustrate the use of a probabilistic programming language that automates inference in existing simulators. Neither the full capabilities of this tool for automating inference nor its utility for planning is widely disseminated at the current time. Timely gains in understanding about how such simulation-based models and inference automation tools applied in support of policymaking could lead to less economically damaging policy prescriptions, particularly during the current COVID-19 pandemic.
We demonstrate the ability of statistical data assimilation to identify the measurements required for accurate state and parameter estimation in an epidemiological model for the novel coronavirus disease COVID-19. Our context is an effort to inform policy regarding social behavior, to mitigate strain on hospital capacity. The model unknowns are taken to be: the time-varying transmission rate, the fraction of exposed cases that require hospitalization, and the time-varying detection probabilities of new asymptomatic and symptomatic cases. In simulations, we obtain accurate estimates of undetected (that is, unmeasured) infectious populations, by measuring the detected cases together with the recovered and dead - and without assumed knowledge of the detection rates. Given a noiseless measurement of the recovered population, excellent estimates of all quantities are obtained using a temporal baseline of 101 days, with the exception of the time-varying transmission rate at times prior to the implementation of social distancing. With low noise added to the recovered population, accurate state estimates require a lengthening of the temporal baseline of measurements. Estimates of all parameters are sensitive to the contamination, highlighting the need for accurate and uniform methods of reporting. The aim of this paper is to exemplify the power of SDA to determine what properties of measurements will yield estimates of unknown parameters to a desired precision, in a model with the complexity required to capture important features of the COVID-19 pandemic.
The occurrence and distributions of wildlife populations and communities are shifting as a result of global changes. To evaluate whether these shifts are negatively impacting biodiversity processes, it is critical to monitor the status, trends, and effects of environmental variables on entire communities. However, modeling the dynamics of multiple species simultaneously can require large amounts of diverse data, and few modeling approaches exist to simultaneously provide species and community level inferences. We present an integrated community occupancy model (ICOM) that unites principles of data integration and hierarchical community modeling in a single framework to provide inferences on species-specific and community occurrence dynamics using multiple data sources. We use simulations to compare the ICOM to previously developed hierarchical community occupancy models and single species integrated distribution models. We then apply our model to assess the occurrence and biodiversity dynamics of foliage-gleaning birds in the White Mountain National Forest in the northeastern USA from 2010-2018 using three independent data sources. Simulations reveal that integrating multiple data sources in the ICOM increased precision and accuracy of species and community level inferences compared to single data source models, although benefits of integration were dependent on data source quality (e.g., amount of replication). Compared to single species models, the ICOM yielded more precise species-level estimates. Within our case study, the ICOM had the highest out-of-sample predictive performance compared to single species models and models that used only a subset of the three data sources. The ICOM offers an attractive approach to estimate species and biodiversity dynamics, which is additionally valuable to inform management objectives of both individual species and their broader communities.
A molecular dynamics calculation of the amino acid polar requirement is presented and used to score the canonical genetic code. Monte Carlo simulation shows that this computational polar requirement has been optimized by the canonical genetic code more than any previously-known measure. These results strongly support the idea that the genetic code evolved from a communal state of life prior to the root of the modern ribosomal tree of life.
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