16 research outputs found
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