Transmission eigenvalues and thermoacoustic tomography

The spectrum of the interior transmission problem is related to the unique determination of the acoustic properties of a body in thermoacoustic imaging. Under a non-trapping hypothesis, we show that sparsity of the interior transmission spectrum implies a range separation condition for the thermoacoustic operator. In odd dimension greater than or equal to three, we prove that the transmission spectrum for a pair of radially symmetric non-trapping sound speeds is countable, and conclude that the ranges of the associated thermoacoustic maps have only trivial intersection

Transmission Eigenvalues and Thermoacoustic Tomography

The spectrum of the interior transmission problem is related to the unique determination of the acoustic properties of a body in thermoacoustic imaging. Under a non-trapping hypothesis, we show that sparsity of the interior transmission spectrum implies a range separation condition for the thermoacoustic operator. In odd dimensions greater than or equal to three, we prove that the interior transmission spectrum for a pair of radially symmetric non-trapping sound speeds is countable, and conclude that the ranges of the associated thermoacoustic maps have only trivial intersection.Keywords: Radial Symmetry, Hybrid Imaging Methods, Interior Transmission Problem, Acoustics, Transmission Eigenvalues, Thermoacoustic Tomograph

Forecasting the 2013--2014 Influenza Season using Wikipedia

Infectious diseases are one of the leading causes of morbidity and mortality around the world; thus, forecasting their impact is crucial for planning an effective response strategy. According to the Centers for Disease Control and Prevention (CDC), seasonal influenza affects between 5% to 20% of the U.S. population and causes major economic impacts resulting from hospitalization and absenteeism. Understanding influenza dynamics and forecasting its impact is fundamental for developing prevention and mitigation strategies. We combine modern data assimilation methods with Wikipedia access logs and CDC influenza like illness (ILI) reports to create a weekly forecast for seasonal influenza. The methods are applied to the 2013--2014 influenza season but are sufficiently general to forecast any disease outbreak, given incidence or case count data. We adjust the initialization and parametrization of a disease model and show that this allows us to determine systematic model bias. In addition, we provide a way to determine where the model diverges from observation and evaluate forecast accuracy. Wikipedia article access logs are shown to be highly correlated with historical ILI records and allow for accurate prediction of ILI data several weeks before it becomes available. The results show that prior to the peak of the flu season, our forecasting method projected the actual outcome with a high probability. However, since our model does not account for re-infection or multiple strains of influenza, the tail of the epidemic is not predicted well after the peak of flu season has past.Comment: Second version. In previous version 2 figure references were compiling wrong due to error in latex sourc

Results from the centers for disease control and prevention's predict the 2013-2014 Influenza Season Challenge

Background: Early insights into the timing of the start, peak, and intensity of the influenza season could be useful in planning influenza prevention and control activities. To encourage development and innovation in influenza forecasting, the Centers for Disease Control and Prevention (CDC) organized a challenge to predict the 2013-14 Unites States influenza season. Methods: Challenge contestants were asked to forecast the start, peak, and intensity of the 2013-2014 influenza season at the national level and at any or all Health and Human Services (HHS) region level(s). The challenge ran from December 1, 2013-March 27, 2014; contestants were required to submit 9 biweekly forecasts at the national level to be eligible. The selection of the winner was based on expert evaluation of the methodology used to make the prediction and the accuracy of the prediction as judged against the U.S. Outpatient Influenza-like Illness Surveillance Network (ILINet). Results: Nine teams submitted 13 forecasts for all required milestones. The first forecast was due on December 2, 2013; 3/13 forecasts received correctly predicted the start of the influenza season within one week, 1/13 predicted the peak within 1 week, 3/13 predicted the peak ILINet percentage within 1 %, and 4/13 predicted the season duration within 1 week. For the prediction due on December 19, 2013, the number of forecasts that correctly forecasted the peak week increased to 2/13, the peak percentage to 6/13, and the duration of the season to 6/13. As the season progressed, the forecasts became more stable and were closer to the season milestones. Conclusion: Forecasting has become technically feasible, but further efforts are needed to improve forecast accuracy so that policy makers can reliably use these predictions. CDC and challenge contestants plan to build upon the methods developed during this contest to improve the accuracy of influenza forecasts. © 2016 The Author(s)

A network-patch methodology for adapting agent-based models for directly transmitted disease to mosquito-borne disease

© 2015 The Author(s). Published by Taylor & Francis. Mosquito-borne diseases cause significant public health burden and are widely re-emerging or emerging. Understanding, predicting, and mitigating the spread of mosquito-borne disease in diverse populations and geographies are ongoing modelling challenges. We propose a hybrid network-patch model for the spread of mosquito-borne pathogens that accounts for individual movement through mosquito habitats, extending the capabilities of existing agent-based models (ABMs) to include vector-borne diseases. The ABM are coupled with differential equations representing ‘clouds’ of mosquitoes in patches accounting for mosquito ecology. We adapted an ABM for humans using this method and investigated the importance of heterogeneity in pathogen spread, motivating the utility of models of individual behaviour. We observed that the final epidemic size is greater in patch models with a high risk patch frequently visited than in a homogeneous model. Our hybrid model quantifies the importance of the heterogeneity in the spread of mosquito-borne pathogens, guiding mitigation strategies