A linear noise approximation for stochastic epidemic models fit to partially observed incidence counts

Detecting changes in the transmission rate of a stochastic epidemic model

Throughout the course of an epidemic, the rate at which disease spreads varies with behavioral changes, the emergence of new disease variants, and the introduction of mitigation policies. Estimating such changes in transmission rates can help us better model and predict the dynamics of an epidemic, and provide insight into the efficacy of control and intervention strategies. We present a method for likelihood-based estimation of parameters in the stochastic susceptible-infected-removed model under a time-inhomogeneous transmission rate comprised of piecewise constant components. In doing so, our method simultaneously learns change points in the transmission rate via a Markov chain Monte Carlo algorithm. The method targets the exact model posterior in a difficult missing data setting given only partially observed case counts over time. We validate performance on simulated data before applying our approach to data from an Ebola outbreak in Western Africa and COVID-19 outbreak on a university campus.

Incorporating testing volume into estimation of effective reproduction number dynamics

Branching process inspired models are widely used to estimate the effective reproduction number-a useful summary statistic describing an infectious disease outbreak-using counts of new cases. Case data is a real-time indicator of changes in the reproduction number, but is challenging to work with because cases fluctuate due to factors unrelated to the number of new infections. We develop a new model that incorporates the number of diagnostic tests as a surveillance model covariate. Using simulated data and data from the SARS-CoV-2 pandemic in California, we demonstrate that incorporating tests leads to improved performance over the state of the art.

Fitting a stochastic model of intensive care occupancy to noisy hospitalization time series during the COVID-19 pandemic

Intensive care occupancy is an important indicator of health care stress that has been used to guide policy decisions during the COVID-19 pandemic. Toward reliable decision-making as a pandemic progresses, estimating the rates at which patients are admitted to and discharged from hospitals and intensive care units (ICUs) is crucial. Since individual-level hospital data are rarely available to modelers in each geographic locality of interest, it is important to develop tools for inferring these rates from publicly available daily numbers of hospital and ICU beds occupied. We develop such an estimation approach based on an immigration-death process that models fluctuations of ICU occupancy. Our flexible framework allows for immigration and death rates to depend on covariates, such as hospital bed occupancy and daily SARS-CoV-2 test positivity rate, which may drive changes in hospital ICU operations. We demonstrate via simulation studies that the proposed method performs well on noisy time series data and apply our statistical framework to hospitalization data from the University of California, Irvine (UCI) Health and Orange County, California. By introducing a likelihood-based framework where immigration and death rates can vary with covariates, we find, through rigorous model selection, that hospitalization and positivity rates are crucial covariates for modeling ICU stay dynamics and validate our per-patient ICU stay estimates using anonymized patient-level UCI hospital data.

Quantifying Invasive Pest Dynamics through Inference of a Two-Node Epidemic Network Model

Invasive woodland pests have substantial ecological, economic, and social impacts, harming biodiversity and ecosystem services. Mathematical modelling informed by Bayesian inference can deepen our understanding of the fundamental behaviours of invasive pests and provide predictive tools for forecasting future spread. A key invasive pest of concern in the UK is the oak processionary moth (OPM). OPM was established in the UK in 2006; it is harmful to both oak trees and humans, and its infestation area is continually expanding. Here, we use a computational inference scheme to estimate the parameters for a two-node network epidemic model to describe the temporal dynamics of OPM in two geographically neighbouring parks (Bushy Park and Richmond Park, London). We show the applicability of such a network model to describing invasive pest dynamics and our results suggest that the infestation within Richmond Park has largely driven the infestation within Bushy Park.

Inference for epidemic models with time-varying infection rates: Tracking the dynamics of oak processionary moth in the UK

Invasive pests pose a great threat to forest, woodland, and urban tree ecosystems. The oak processionary moth (OPM) is a destructive pest of oak trees, first reported in the UK in 2006. Despite great efforts to contain the outbreak within the original infested area of South‐East England, OPM continues to spread.

Here, we analyze data consisting of the numbers of OPM nests removed each year from two parks in London between 2013 and 2020. Using a state‐of‐the‐art Bayesian inference scheme, we estimate the parameters for a stochastic compartmental SIR (susceptible, infested, and removed) model with a time‐varying infestation rate to describe the spread of OPM.

We find that the infestation rate and subsequent basic reproduction number have remained constant since 2013 (with R0 between one and two). This shows further controls must be taken to reduce R0 below one and stop the advance of OPM into other areas of England.

Synthesis. Our findings demonstrate the applicability of the SIR model to describing OPM spread and show that further controls are needed to reduce the infestation rate. The proposed statistical methodology is a powerful tool to explore the nature of a time‐varying infestation rate, applicable to other partially observed time series epidemic data.

A hybrid stochastic model and its Bayesian identification for infectious disease screening in a university campus with application to massive COVID-19 screening at the University of Liège

Amid the COVID-19 pandemic, universities are implementing various prevention and mitigation measures. Identifying and isolating infectious individuals by using screening testing is one such a measure that can contribute to reducing spread. Here, we propose a hybrid stochastic model for infectious disease transmission in a university campus with screening testing and its surrounding community. Based on a compartmental modeling strategy, this hybrid stochastic model represents the evolution of the infectious disease and its transmission using continuous-time stochastic dynamics, and it represents the screening testing as discrete stochastic events. We also develop, in a Bayesian framework, the identification of parameters of this hybrid stochastic model, including transmission rates. These parameters were identified from the screening test data for the university population and observed incidence counts for the surrounding community. We implement the exploration of the Bayesian posterior using a machine-learning simulation-based inference approach. The proposed methodology was applied in a retrospective modeling study of a massive COVID-19 screening conducted at the University of Liège in Fall 2020. The emphasis of the paper is on the development of the hybrid stochastic model to assess the impact of screening testing as a measure to reduce spread. The hybrid stochastic model allows various factors to be represented and examined, such as interplay with the surrounding community, variability of the transmission dynamics, the rate of participation in the screening testing, the test sensitivity, the test frequency, the diagnosis delay, and compliance with isolation. The application in the retrospective modeling study suggests that a high rate of participation and a high test frequency are important factors to reduce spread.