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

Stochastic epidemic models (SEMs) fit to incidence data are critical to elucidating outbreak dynamics, shaping response strategies, and preparing for future epidemics. SEMs typically represent counts of individuals in discrete infection states using Markov jump processes (MJPs), but are computationally challenging as imperfect surveillance, lack of subject-level information, and temporal coarseness of the data obscure the true epidemic. Analytic integration over the latent epidemic process is impossible, and integration via Markov chain Monte Carlo (MCMC) is cumbersome due to the dimensionality and discreteness of the latent state space. Simulation-based computational approaches can address the intractability of the MJP likelihood, but are numerically fragile and prohibitively expensive for complex models. A linear noise approximation (LNA) that approximates the MJP transition density with a Gaussian density has been explored for analyzing prevalence data in large-population settings, but requires modification for analyzing incidence counts without assuming that the data are normally distributed. We demonstrate how to reparameterize SEMs to appropriately analyze incidence data, and fold the LNA into a data augmentation MCMC framework that outperforms deterministic methods, statistically, and simulation-based methods, computationally. Our framework is computationally robust when the model dynamics are complex and applies to a broad class of SEMs. We evaluate our method in simulations that reflect Ebola, influenza, and SARS-CoV-2 dynamics, and apply our method to national surveillance counts from the 2013--2015 West Africa Ebola outbreak

Efficient data augmentation for fitting stochastic epidemic models to prevalence data

Stochastic epidemic models describe the dynamics of an epidemic as a disease spreads through a population. Typically, only a fraction of cases are observed at a set of discrete times. The absence of complete information about the time evolution of an epidemic gives rise to a complicated latent variable problem in which the state space size of the epidemic grows large as the population size increases. This makes analytically integrating over the missing data infeasible for populations of even moderate size. We present a data augmentation Markov chain Monte Carlo (MCMC) framework for Bayesian estimation of stochastic epidemic model parameters, in which measurements are augmented with subject-level disease histories. In our MCMC algorithm, we propose each new subject-level path, conditional on the data, using a time-inhomogeneous continuous-time Markov process with rates determined by the infection histories of other individuals. The method is general, and may be applied, with minimal modifications, to a broad class of stochastic epidemic models. We present our algorithm in the context of multiple stochastic epidemic models in which the data are binomially sampled prevalence counts, and apply our method to data from an outbreak of influenza in a British boarding school

Semi-parametric modeling of SARS-CoV-2 transmission in Orange County, California using tests, cases, deaths, and seroprevalence data

Mechanistic modeling of SARS-CoV-2 transmission dynamics and frequently estimating model parameters using streaming surveillance data are important components of the pandemic response toolbox. However, transmission model parameter estimation can be imprecise, and sometimes even impossible, because surveillance data are noisy and not informative about all aspects of the mechanistic model. To partially overcome this obstacle, we propose a Bayesian modeling framework that integrates multiple surveillance data streams. Our model uses both SARS-CoV-2 diagnostics test and mortality time series to estimate our model parameters, while also explicitly integrating seroprevalence data from cross-sectional studies. Importantly, our data generating model for incidence data takes into account changes in the total number of tests performed. We model transmission rate, infection-to-fatality ratio, and a parameter controlling a functional relationship between the true case incidence and the fraction of positive tests as time-varying quantities and estimate changes of these parameters nonparameterically. We apply our Bayesian data integration method to COVID-19 surveillance data collected in Orange County, California between March, 2020 and March, 2021 and find that 33-62% of the Orange County residents experienced SARS-CoV-2 infection by the end of February, 2021. Despite this high number of infections, our results show that the abrupt end of the winter surge in January, 2021, was due to both behavioral changes and a high level of accumulated natural immunity.Comment: 37 pages, 16 pages of main text, including 5 figures, 1 tabl

Bayesian Modeling of Partially Observed Epidemic Count Data

Thesis (Ph.D.)--University of Washington, 2018Epidemic count data reported by public health surveillance systems reflect the incidence or prevalence of an infectious agent as it spreads through a population. They are a primary source of information for shaping response strategies and for predicting how an outbreak will evolve. Incidence and prevalence counts are often the only source of information about historical outbreaks, or outbreaks in resource limited settings, which are of interest for researchers seeking to develop an understanding of disease transmission during ``peace time", with an eye on preparing for future outbreaks. The absence of subject--level information and the systematic underreporting of cases complicate the task of disentangling whether the data arose from a severe outbreak, observed with low fidelity, or a mild outbreak were most cases were detected. The magnitude of the missing data and the high dimensional state space of the latent epidemic process present challenges for fitting epidemic models that appropriately quantify the stochastic aspects of the transmission dynamics. In this dissertation, we develop computational algorithms for fitting stochastic epidemic models to partially observed incidence and prevalence data. Our algorithms are not specific to particular model dynamics, but rather apply to a broad class of commonly used stochastic epidemic models, including models that allow for time--inhomogeneous transmission dynamics. We use our methods to analyze data from an outbreak of influenza in a British boarding school, the 2014--2015 outbreak of Ebola in West Africa, and the 2009--2011 A(H1N1) influenza pandemic in Finland

Comparison of the transmission efficiency and plague progression dynamics associated with two mechanisms by which fleas transmit Yersinia pestis.

Yersinia pestis can be transmitted by fleas during the first week after an infectious blood meal, termed early-phase or mass transmission, and again after Y. pestis forms a cohesive biofilm in the flea foregut that blocks normal blood feeding. We compared the transmission efficiency and the progression of infection after transmission by Oropsylla montana fleas at both stages. Fleas were allowed to feed on mice three days after an infectious blood meal to evaluate early-phase transmission, or after they had developed complete proventricular blockage. Transmission was variable and rather inefficient by both modes, and the odds of early-phase transmission was positively associated with the number of infected fleas that fed. Disease progression in individual mice bitten by fleas infected with a bioluminescent strain of Y. pestis was tracked. An early prominent focus of infection at the intradermal flea bite site and dissemination to the draining lymph node(s) soon thereafter were common features, but unlike what has been observed in intradermal injection models, this did not invariably lead to further systemic spread and terminal disease. Several of these mice resolved the infection without progression to terminal sepsis and developed an immune response to Y. pestis, particularly those that received an intermediate number of early-phase flea bites. Furthermore, two distinct types of terminal disease were noted: the stereotypical rapid onset terminal disease within four days, or a prolonged onset preceded by an extended, fluctuating infection of the lymph nodes before eventual systemic dissemination. For both modes of transmission, bubonic plague rather than primary septicemic plague was the predominant disease outcome. The results will help to inform mathematical models of flea-borne plague dynamics used to predict the relative contribution of the two transmission modes to epizootic outbreaks that erupt periodically from the normal enzootic background state