In this article, we introduce the R package EpiILM, which provides tools for simulation from, and inference for, discrete-time individual-level models of infectious disease transmission proposed by Deardon et al. (2010). The inference is set in a Bayesian framework and is carried out via Metropolis-Hastings Markov chain Monte Carlo (MCMC). For its fast implementation, key functions are coded in Fortran. Both spatial and contact network models are implemented in the package and can be set in either susceptible-infected (SI) or susceptible-infected-removed (SIR) compartmental frameworks. The use of the package is demonstrated through examples involving both simulated and real data.
This paper describes the R package EpiILMCT, which allows users to study the spread of infectious disease using continuous time individual level models (ILMs). The package provides tools for simulation from continuous time ILMs that are based on either spatial demographic, contact network, or a combination of both of them, and for the graphical summarization of epidemics. Model fitting is carried out within a Bayesian Markov Chain Monte Carlo (MCMC) framework. The continuous time ILMs can be implemented within either susceptible-infected-removed (SIR) or susceptible-infected-notified-removed (…
We introduce Pathogen.jl for simulation and inference of transmission network individual level models (TN-ILMs) of infectious disease spread in continuous time. TN-ILMs can be used to jointly infer transmission networks, event times, and model parameters within a Bayesian framework via Markov chain Monte Carlo (MCMC). We detail our specific strategies for conducting MCMC for TN-ILMs, and our implementation of these strategies in the Julia package, Pathogen.jl, which leverages key features of the Julia language. We provide an example using Pathogen.jl to simulate an epidemic following a suscept…
Stochastic compartmental models are important tools for understanding the course of infectious diseases epidemics in populations and in prospective evaluation of intervention policies. However, calculating the likelihood for discretely observed data from even simple models -- such as the ubiquitous susceptible-infectious-removed (SIR) model -- has been considered computationally intractable, since its formulation almost a century ago. Recently researchers have proposed methods to circumvent this limitation through data augmentation or approximation, but these approaches often suffer from high …
We propose a mathematical model based on probability theory to optimize COVID-19 testing by a multi-step batch testing approach with variable batch sizes. This model and simulation tool dramatically increase the efficiency and efficacy of the tests in a large population at a low cost, particularly when the infection rate is low. The proposed method combines statistical modeling with numerical methods to solve nonlinear equations and obtain optimal batch sizes at each step of tests, with the flexibility to incorporate geographic and demographic information. In theory, this method substantially …
A reasonable prediction of infectious diseases transmission process under different disease control strategies is an important reference point for policy makers. Here we established a dynamic transmission model via Python and realized comprehensive regulation of disease control measures. We classified government interventions into three categories and introduced three parameters as descriptions for the key points in disease control, these being intraregional growth rate, interregional communication rate, and detection rate of infectors. Our simulation predicts the infection by COVID-19 in the …
A class of stochastic vector-borne infectious disease models is derived and studied. The class type is determined by a general nonlinear incidence rate of the disease. The disease spreads in a highly random environment with variability from the disease transmission and natural death rates. Other sources of variability include the random delays of disease incubation inside the vector and the human being, and also the random delay due to the period of effective acquired immunity against the disease. The basic reproduction number and other threshold conditions for disease eradication are computed…
Spatial big data have the "velocity," "volume," and "variety" of big data sources and additional geographic information about the record. Digital data sources, such as medical claims, mobile phone call data records, and geo-tagged tweets, have entered infectious disease epidemiology as novel sources of data to complement traditional infectious disease surveillance. In this work, we provide examples of how spatial big data have been used thus far in epidemiological analyses and describe opportunities for these sources to improve public health coordination and disease mitigation strategies. In a…
Infectious disease models can be of great use for understanding the underlying mechanisms that influence the spread of diseases and predicting future disease progression. Modeling has been increasingly used to evaluate the potential impact of different control measures and to guide public health policy decisions. In recent years, there has been rapid progress in developing spatio-temporal modeling of infectious diseases and an example of such recent developments is the discrete time individual-level models (ILMs). These models are well developed and provide a common framework for modeling many…
Routine public health surveillance of notifiable infectious diseases gives rise to weekly counts of reported cases -- possibly stratified by region and/or age group. We investigate how an age-structured social contact matrix can be incorporated into a spatio-temporal endemic-epidemic model for infectious disease counts. To illustrate the approach, we analyze the spread of norovirus gastroenteritis over 6 age groups within the 12 districts of Berlin, 2011-2015, using contact data from the POLYMOD study. The proposed age-structured model outperforms alternative scenarios with homogeneous or no m…
Forecasting transmission of infectious diseases, especially for vector-borne diseases, poses unique challenges for researchers. Behaviors of and interactions between viruses, vectors, hosts, and the environment each play a part in determining the transmission of a disease. Public health surveillance systems and other sources provide valuable data that can be used to accurately forecast disease incidence. However, many aspects of common infectious disease surveillance data are imperfect: cases may be reported with a delay or in some cases not at all, data on vectors may not be available, and ca…
Spatio-temporal counts of infectious disease cases often contain an excess of zeros. With existing zero inflated count models applied to such data it is difficult to quantify space-time heterogeneity in the effects of disease spread between areas. Also, existing methods do not allow for separate dynamics to affect the reemergence and persistence of the disease. As an alternative, we develop a new zero-state coupled Markov switching negative binomial model, under which the disease switches between periods of presence and absence in each area through a series of partially hidden nonhomogeneous M…
Randomized trials of infectious disease interventions, such as vaccines, often focus on groups of connected or potentially interacting individuals. When the pathogen of interest is transmissible between study subjects, interference may occur: individual infection outcomes may depend on treatments received by others. Epidemiologists have defined the primary causal effect of interest -- called the "susceptibility effect" -- as a contrast in infection risk under treatment versus no treatment, while holding exposure to infectiousness constant. A related quantity -- the "direct effect" -- is define…
Early detection of person-to-person transmission of emerging infectious diseases such as avian influenza is crucial for containing pandemics. We developed a simple permutation test and its refined version for this purpose. A simulation study shows that the refined permutation test is as powerful as or outcompetes the conventional test built on asymptotic theory, especially when the sample size is small. In addition, our resampling methods can be applied to a broad range of problems where an asymptotic test is not available or fails. We also found that decent statistical power could be attained…
This paper is concerned with the application of recent statistical advances to inference of infectious disease dynamics. We describe the fitting of a class of epidemic models using Hamiltonian Monte Carlo and Variational Inference as implemented in the freely available Stan software. We apply the two methods to real data from outbreaks as well as routinely collected observations. Our results suggest that both inference methods are computationally feasible in this context, and show a trade-off between statistical efficiency versus computational speed. The latter appears particularly relevant fo…
Motivated by foot-and-mouth disease (FMD) outbreak data from Turkey, we develop a model to estimate disease risk based on a space-time record of outbreaks. The spread of infectious disease in geographical units depends on both transmission between neighbouring units and the intrinsic susceptibility of each unit to an outbreak. Spatially correlated susceptibility may arise from known factors, such as population density, or unknown (or unmeasured) factors such as commuter flows, environmental conditions, or health disparities. Our framework accounts for both space-time transmission and susceptib…
A spatial analysis of COVID-19 reported cases in the Gauteng province, South Africa: Identifying wards to be targeted early in future infectious diseases outbreak
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 …
We propose a new parametric time-varying shared frailty model to represent changes over time in population heterogeneity, for use with bivariate current status data. The model uses a power transformation of a time-invariant frailty $U$, and is particularly convenient when $U$ is a member of the generalized gamma family. This model avoids some shortcomings of a previously suggested time-varying frailty model, notably time-dependent support. We describe some key properties of the model, including its relative frailty variance function in different settings and how the model can be fitted to data…
Multivariate count time series models are an important tool for the analysis and prediction of infectious disease spread. We consider the endemic-epidemic framework, an autoregressive model class for infectious disease surveillance counts, and replace the default autoregression on counts from the previous time period with more flexible weighting schemes inspired by discrete-time serial interval distributions. We employ three different parametric formulations, each with an additional unknown weighting parameter estimated via a profile likelihood approach, and compare them to an unrestricted non…
Infectious disease forecasting is of great interest to the public health community and policymakers, since forecasts can provide insight into disease dynamics in the near future and inform interventions. Due to delays in case reporting, however, forecasting models may often underestimate the current and future disease burden. In this paper, we propose a general framework for addressing reporting delay in disease forecasting efforts with the goal of improving forecasts. We propose strategies for leveraging either historical data on case reporting or external internet-based data to estimate the …
Causal identification of treatment effects for infectious disease outcomes in interconnected populations is challenging because infection outcomes may be transmissible to others, and treatment given to one individual may affect others' outcomes. Contagion, or transmissibility of outcomes, complicates standard conceptions of treatment interference in which an intervention delivered to one individual can affect outcomes of others. Several statistical frameworks have been proposed to measure causal treatment effects in this setting, including structural transmission models, mediation-based partne…
In regard to infectious diseases socioeconomic determinants are strongly associated with differential exposure and susceptibility however they are seldom accounted for by standard compartmental infectious disease models. These associations are explored here with a novel compartmental infectious disease model which, stratified by deprivation and age, accounts for population-level behaviour including social mixing patterns. As an exemplar using a fully Bayesian approach our model is fitted, in real-time if required, to the UKHSA COVID-19 community testing case data from England. Metrics includin…
We propose a framework for Bayesian non-parametric estimation of the rate at which new infections occur assuming that the epidemic is partially observed. The developed methodology relies on modelling the rate at which new infections occur as a function which only depends on time. Two different types of prior distributions are proposed namely using step-functions and B-splines. The methodology is illustrated using both simulated and real datasets and we show that certain aspects of the epidemic such as seasonality and super-spreading events are picked up without having to explicitly incorporate…
A Counterfactual Framework for Estimating Infectious Disease Prevalence under Repeated Testing with Symptomatic and Contact-Tracing Components
Division of Biostatistics, College of Public Health, The Ohio State University（俄亥俄州立大学公共卫生学院生物统计系）；Department of Medical Epidemiology and Biostatistics, Karolinska Institutet（卡罗林斯卡医学院医学流行病学与生物统计系）
