Bayesian parameter inference for dynamic infectious disease modelling: rotavirus in Germany

Inference under superspreading: Determinants of SARS-CoV-2 transmission in Germany

Superspreading, under-reporting, reporting delay, and confounding complicate statistical inference on determinants of disease transmission. A model that accounts for these factors within a Bayesian framework is estimated using German Covid-19 surveillance data. Compartments based on date of symptom onset, location, and age group allow to identify age-specific changes in transmission, adjusting for weather, reported prevalence, and testing and tracing. Several factors were associated with a reduction in transmission: public awareness rising, information on local prevalence, testing and tracing, high temperature, stay-at-home orders, and restaurant closures. However, substantial uncertainty remains for other interventions including school closures and mandatory face coverings. The challenge of disentangling the effects of different determinants is discussed and examined through a simulation study. On a broader perspective, the study illustrates the potential of surveillance data with demographic information and date of symptom onset to improve inference in the presence of under-reporting and reporting delay.

Quantifying Uncertainty in Mechanistic Models of Infectious Disease

This primer describes the statistical uncertainty in mechanistic models and provides R code to quantify it. We begin with an overview of mechanistic models for infectious disease, and then describe the sources of statistical uncertainty in the context of a case study on SARS-CoV-2. We describe the statistical uncertainty as belonging to three categories: data uncertainty, stochastic uncertainty, and structural uncertainty. We demonstrate how to account for each of these via statistical uncertainty measures and sensitivity analyses broadly, as well as in a specific case study on estimating the basic reproductive number, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}${R}_0$\end{document}, for SARS-CoV-2.

Model selection and parameter estimation for dynamic epidemic models via iterated filtering: application to rotavirus in Germany

Despite the wide application of dynamic models in infectious disease epidemiology, the particular modeling of variability in the different model components is often subjective rather than the result of a thorough model selection process. This is in part because inference for a stochastic transmission model can be difficult since the likelihood is often intractable due to partial observability. In this work, we address the question of adequate inclusion of variability by demonstrating a systematic approach for model selection and parameter inference for dynamic epidemic models. For this, we perform inference for six partially observed Markov process models, which assume the same underlying transmission dynamics, but differ with respect to the amount of variability they allow for. The inference framework for the stochastic transmission models is provided by iterated filtering methods, which are readily implemented in the R package pomp by King and others (2016, Statistical inference for partially observed Markov processes via the R package pomp. Journal of Statistical Software69, 1–43). We illustrate our approach on German rotavirus surveillance data from 2001 to 2008, discuss practical difficulties of the methods used and calculate a model based estimate for the basic reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$R_0$\end{document} using these data.

COVID-19 outbreak in Wuhan demonstrates the limitations of publicly available case numbers for epidemiological modeling

Epidemiological models are widely used to analyze the spread of diseases such as the global COVID-19 pandemic caused by SARS-CoV-2. However, all models are based on simplifying assumptions and often on sparse data. This limits the reliability of parameter estimates and predictions. In this manuscript, we demonstrate the relevance of these limitations and the pitfalls associated with the use of overly simplistic models. We considered the data for the early phase of the COVID-19 outbreak in Wuhan, China, as an example, and perform parameter estimation, uncertainty analysis and model selection for a range of established epidemiological models. Amongst others, we employ Markov chain Monte Carlo sampling, parameter and prediction profile calculation algorithms. Our results show that parameter estimates and predictions obtained for several established models on the basis of reported case numbers can be subject to substantial uncertainty. More importantly, estimates were often unrealistic and the confidence/credibility intervals did not cover plausible values of critical parameters obtained using different approaches. These findings suggest, amongst others, that standard compartmental models can be overly simplistic and that the reported case numbers provide often insufficient information for obtaining reliable and realistic parameter values, and for forecasting the evolution of epidemics.

A marginal moment matching approach for fitting endemic-epidemic models to underreported disease surveillance counts

Count data are often subject to underreporting, especially in infectious disease surveillance. We propose an approximate maximum likelihood method to fit count time series models from the endemic-epidemic class to underreported data. The approach is based on marginal moment matching where underreported processes are approximated through completely observed processes from the same class. Moreover, the form of the bias when underreporting is ignored or taken into account via multiplication factors is analyzed. Notably, we show that this leads to a downward bias in model-based estimates of the effective reproductive number. A marginal moment matching approach can also be used to account for reporting intervals which are longer than the mean serial interval of a disease. The good performance of the proposed methodology is demonstrated in simulation studies. An extension to time-varying parameters and reporting probabilities is discussed and applied in a case study on weekly rotavirus gastroenteritis counts in Berlin, Germany.

Profile likelihood-based analyses of infectious disease models

Ordinary differential equation models are frequently applied to describe the temporal evolution of epidemics. However, ordinary differential equation models are also utilized in other scientific fields. We summarize and transfer state-of-the art approaches from other fields like Systems Biology to infectious disease models. For this purpose, we use a simple SIR model with data from an influenza outbreak at an English boarding school in 1978 and a more complex model of a vector-borne disease with data from the Zika virus outbreak in Colombia in 2015-2016. Besides parameter estimation using a deterministic multistart optimization approach, a multitude of analyses based on the profile likelihood are presented comprising identifiability analysis and model reduction. The analyses were performed using the freely available modeling framework Data2Dynamics (data2dynamics.org) which has been awarded as best performing within the DREAM6 parameter estimation challenge and in the DREAM7 network reconstruction challenge.

Identifying cost-effective dynamic policies to control epidemics

We describe a mathematical decision model for identifying dynamic health policies for controlling epidemics. These dynamic policies aim to select the best current intervention based on accumulating epidemic data and the availability of resources at each decision point. We propose an algorithm to approximate dynamic policies that optimize the population's net health benefit, a performance measure which accounts for both health and monetary outcomes. We further illustrate how dynamic policies can be defined and optimized for the control of a novel viral pathogen, where a policy maker must decide (i) when to employ or lift a transmission-reducing intervention (e.g. school closure) and (ii) how to prioritize population members for vaccination when a limited quantity of vaccines first become available. Within the context of this application, we demonstrate that dynamic policies can produce higher net health benefit than more commonly described static policies that specify a pre-determined sequence of interventions to employ throughout epidemics. Copyright © 2016 John Wiley & Sons, Ltd.

Estimating dynamic transmission model parameters for seasonal influenza by fitting to age and season-specific influenza-like illness incidence

Dynamic transmission models are essential to design and evaluate control strategies for airborne infections. Our objective was to develop a dynamic transmission model for seasonal influenza allowing to evaluate the impact of vaccinating specific age groups on the incidence of infection, disease and mortality. Projections based on such models heavily rely on assumed 'input' parameter values. In previous seasonal influenza models, these parameter values were commonly chosen ad hoc, ignoring between-season variability and without formal model validation or sensitivity analyses. We propose to directly estimate the parameters by fitting the model to age-specific influenza-like illness (ILI) incidence data over multiple influenza seasons. We used a weighted least squares (WLS) criterion to assess model fit and applied our method to Belgian ILI data over six influenza seasons. After exploring parameter importance using symbolic regression, we evaluated a set of candidate models of differing complexity according to the number of season-specific parameters. The transmission parameters (average R0, seasonal amplitude and timing of the seasonal peak), waning rates and the scale factor used for WLS optimization, influenced the fit to the observed ILI incidence the most. Our results demonstrate the importance of between-season variability in influenza transmission and our estimates are in line with the classification of influenza seasons according to intensity and vaccine matching.

Quantifying Parameter and Structural Uncertainty of Dynamic Disease Transmission Models Using MCMC: An Application to Rotavirus Vaccination in England and Wales

BACKGROUND

Two vaccines (Rotarix and RotaTeq) are highly effective at preventing severe rotavirus disease. Rotavirus vaccination has been introduced in the United Kingdom and other countries partly based on modeling and cost-effectiveness results. However, most of these models fail to account for the uncertainty about several vaccine characteristics and the mechanism of vaccine action.

METHODS

A deterministic dynamic transmission model of rotavirus vaccination in the United Kingdom was developed. This improves on previous models by 1) allowing for 2 different mechanisms of action for Rotarix and RotaTeq, 2) using clinical trial data to understand these mechanisms, and 3) accounting for uncertainty by using Markov Chain Monte Carlo.

RESULTS

In the long run, Rotarix and RotaTeq are predicted to reduce the overall rotavirus incidence by 50% (39%-63%) and 44% (30%-62%), respectively but with an increase in incidence in primary school children and adults up to 25 y of age. The vaccines are estimated to give more protection than 1 or 2 natural infections. The duration of protection is highly uncertain but has only impact on the predicted reduction in rotavirus burden for values lower than 10 y. The 2 vaccine mechanism structures fit equally well with the clinical trial data. Long-term postvaccination dynamics cannot be predicted reliably with the data available.

CONCLUSION

Accounting for the joint uncertainty of several vaccine characteristics resulted in more insight into which of these are crucial for determining the impact of rotavirus vaccination. Data for up to at least 10 y postvaccination and covering older children and adults are crucial to address remaining questions on the impact of widespread rotavirus vaccination.