Using epidemic prevalence data to jointly estimate reproduction and removal

This study proposes a nonhomogeneous birth--death model which captures the dynamics of a directly transmitted infectious disease. Our model accounts for an important aspect of observed epidemic data in which only symptomatic infecteds are observed. The nonhomogeneous birth--death process depends on survival distributions of reproduction and removal, which jointly yield an estimate of the effective reproduction number $R(t)$ as a function of epidemic time. We employ the Burr distribution family for the survival functions and, as special cases, proportional rate and accelerated event-time models are also employed for the parameter estimation procedure. As an example, our model is applied to an outbreak of avian influenza (H7N7) in the Netherlands, 2003, confirming that the conditional estimate of $R(t)$ declined below unity for the first time on day 23 since the detection of the index case.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS270 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Contact intervals, survival analysis of epidemic data, and estimation of R_0

We argue that the time from the onset of infectiousness to infectious contact, which we call the contact interval, is a better basis for inference in epidemic data than the generation or serial interval. Since contact intervals can be right-censored, survival analysis is the natural approach to estimation. Estimates of the contact interval distribution can be used to estimate R_0 in both mass-action and network-based models.Comment: 30 pages, 4 figures; submitted to Biostatistic

Estimation of the basic reproductive number and mean serial interval of a novel pathogen in a small, well-observed discrete population

BACKGROUND:Accurately assessing the transmissibility and serial interval of a novel human pathogen is public health priority so that the timing and required strength of interventions may be determined. Recent theoretical work has focused on making best use of data from the initial exponential phase of growth of incidence in large populations. METHODS:We measured generational transmissibility by the basic reproductive number R0 and the serial interval by its mean Tg. First, we constructed a simulation algorithm for case data arising from a small population of known size with R0 and Tg also known. We then developed an inferential model for the likelihood of these case data as a function of R0 and Tg. The model was designed to capture a) any signal of the serial interval distribution in the initial stochastic phase b) the growth rate of the exponential phase and c) the unique combination of R0 and Tg that generates a specific shape of peak incidence when the susceptible portion of a small population is depleted. FINDINGS:Extensive repeat simulation and parameter estimation revealed no bias in univariate estimates of either R0 and Tg. We were also able to simultaneously estimate both R0 and Tg. However, accurate final estimates could be obtained only much later in the outbreak. In particular, estimates of Tg were considerably less accurate in the bivariate case until the peak of incidence had passed. CONCLUSIONS:The basic reproductive number and mean serial interval can be estimated simultaneously in real time during an outbreak of an emerging pathogen. Repeated application of these methods to small scale outbreaks at the start of an epidemic would permit accurate estimates of key parameters

A Diffusion Approximation for an Epidemic Model

Influenza is one of the most common and severe diseases worldwide. Devastating epidemics actuated by a new subtype of the influenza A virus occur again and again with the most important example given by the Spanish Flu in 1918/19 with more than 27 million deaths. For the development of pandemic plans it is essential to understand the character of the dissemination of the disease. We employ an extended SIR model for a probabilistic analysis of the spatio-temporal spread of influenza in Germany. The inhomogeneous mixing of the population is taken into account by the introduction of a network of subregions, connected according to Germany's commuter and domestic air traffic. The infection dynamics is described by a multivariate diffusion process, the discussion of which is a major part of this report. We furthermore present likelihood-based estimates of the model parameters

A generalized-growth model to characterize the early ascending phase of infectious disease outbreaks

A better characterization of the early growth dynamics of an epidemic is needed to dissect the important drivers of disease transmission. We introduce a 2-parameter generalized-growth model to characterize the ascending phase of an outbreak and capture epidemic profiles ranging from sub-exponential to exponential growth. We test the model against empirical outbreak data representing a variety of viral pathogens and provide simulations highlighting the importance of sub-exponential growth for forecasting purposes. We applied the generalized-growth model to 20 infectious disease outbreaks representing a range of transmission routes. We uncovered epidemic profiles ranging from very slow growth (p=0.14 for the Ebola outbreak in Bomi, Liberia (2014)) to near exponential (p>0.9 for the smallpox outbreak in Khulna (1972), and the 1918 pandemic influenza in San Francisco). The foot-and-mouth disease outbreak in Uruguay displayed a profile of slower growth while the growth pattern of the HIV/AIDS epidemic in Japan was approximately linear. The West African Ebola epidemic provided a unique opportunity to explore how growth profiles vary by geography; analysis of the largest district-level outbreaks revealed substantial growth variations (mean p=0.59, range: 0.14-0.97). Our findings reveal significant variation in epidemic growth patterns across different infectious disease outbreaks and highlights that sub-exponential growth is a common phenomenon. Sub-exponential growth profiles may result from heterogeneity in contact structures or risk groups, reactive behavior changes, or the early onset of interventions strategies, and consideration of "deceleration parameters" may be useful to refine existing mathematical transmission models and improve disease forecasts.Comment: 31 pages, 9 Figures, 1 Supp. Figure, 1 Table, final accepted version (in press), Epidemics - The Journal on Infectious Disease Dynamics, 201