Background: Twitter has shown some usefulness in predicting influenza cases on a weekly basis in multiple countries and on different geographic scales. Recently, Broniatowski and colleagues suggested Twitter's relevance at the city-level for New York City. Here, we look to dive deeper into the case of New York City by analyzing daily Twitter data from temporal and spatiotemporal perspectives. Also, through manual coding of all tweets, we look to gain qualitative insights that can help direct future automated searches.
Dengue is a common and growing problem worldwide, with an estimated 70–140 million cases per year. Traditional, healthcare-based, government-implemented dengue surveillance is resource intensive and slow. As global Internet use has increased, novel, Internet-based disease monitoring tools have emerged. Google Dengue Trends (GDT) uses near real-time search query data to create an index of dengue incidence that is a linear proxy for traditional surveillance. Studies have shown that GDT correlates highly with dengue incidence in multiple countries on a large spatial scale. This study addresses the heterogeneity of GDT at smaller spatial scales, assessing its accuracy at the state-level in Mexico and identifying factors that are associated with its accuracy. We used Pearson correlation to estimate the association between GDT and traditional dengue surveillance data for Mexico at the national level and for 17 Mexican states. Nationally, GDT captured approximately 83% of the variability in reported cases over the 9 study years. The correlation between GDT and reported cases varied from state to state, capturing anywhere from 1% of the variability in Baja California to 88% in Chiapas, with higher accuracy in states with higher dengue average annual incidence. A model including annual average maximum temperature, precipitation, and their interaction accounted for 81% of the variability in GDT accuracy between states. This climate model was the best indicator of GDT accuracy, suggesting that GDT works best in areas with intense transmission, particularly where local climate is well suited for transmission. Internet accessibility (average ∼36%) did not appear to affect GDT accuracy. While GDT seems to be a less robust indicator of local transmission in areas of low incidence and unfavorable climate, it may indicate cases among travelers in those areas. Identifying the strengths and limitations of novel surveillance is critical for these types of data to be used to make public health decisions and forecasting models.
Search query information from a clinician's database, UpToDate, is shown to predict influenza epidemics in the United States in a timely manner. Our results show that digital disease surveillance tools based on experts' databases may be able to provide an alternative, reliable, and stable signal for accurate predictions of influenza outbreaks.
Background: Google Flu Trends (GFT) claimed to generate real-time, valid predictions of population influenza-like illness (ILI) using search queries, heralding acclaim and replication across public health. However, recent studies have questioned the validity of GFT. Purpose: To propose an alternative methodology that better realizes the potential of GFT, with collateral value for digital disease detection broadly. Methods: Our alternative method automatically selects specific queries to monitor and autonomously updates the model each week as new information about CDC-reported ILI becomes available, as developed in 2013. Root mean squared errors (RMSEs) and Pearson correlations comparing predicted ILI (proportion of patient visits indicative of ILI) with subsequently observed ILI were used to judge model performance. Results: During the height of the H1N1 pandemic (August 2 to December 22, 2009) and the 2012-2013 season (September 30, 2012, to April 12, 2013), GFT's predictions had RMSEs of 0.023 and 0.022 (i.e., hypothetically, if GFT predicted 0.061 ILI one week, it is expected to err by 0.023) and correlations of r=0.916 and 0.927. Our alternative method had RMSEs of 0.006 and 0.009, and correlations of r=0.961 and 0.919 for the same periods. Critically, during these important periods, the alternative method yielded more accurate ILI predictions every week, and was typically more accurate during other influenza seasons. Conclusions: GFT may be inaccurate, but improved methodologic underpinnings can yield accurate predictions. Applying similar methods elsewhere can improve digital disease detection, with broader transparency, improved accuracy, and real-world public health impacts.
It is of crucial importance to be able to identify the location of atmospheric pollution sources in our planet. Global models of atmospheric transport in combination with diverse Earth observing systems are a natural choice to achieve this goal. It is shown that the ability to successfully reconstruct the location and magnitude of an instantaneous source in global chemical transport models (CTMs) decreases rapidly as a function of the time interval between the pollution release and the observation time. A simple way to quantitatively characterize this phenomenon is proposed based on the effective -undesired- numerical diffusion present in current Eulerian CTMs and verified using idealized numerical experiments. The approach presented consists of using the adjoint-based optimization method in a state-of-the-art CTM, GEOS-Chem, to reconstruct the location and magnitude of a realistic pollution plume for multiple time scales. The findings obtained from these numerical experiments suggest a time scale of 2 days after which the accuracy of the adjoint-based optimization methodology is compromised considerably in current global CTMs. In conjunction with the mean atmospheric velocity, the aforementioned time scale leads to an estimate of a length scale of about 1700km, downwind from the source, beyond which measurements, in conjunction with current global CTMs, may not be successfully utilized to reconstruct continuous-in-time sources. The approach presented here can be utilized to characterize the capabilities and limitations of adjoint-based optimization inversions in other regional and global Eulerian CTMs.
We study the numerical recovery of Manning's roughness coefficient for the diffusive wave approximation of the shallow water equation. We describe a conjugate gradient method for the numerical inversion. Numerical results for one-dimensional model are presented to illustrate the feasibility of the approach. Also we provide a proof of the differentiability of the weak form with respect to the coefficient as well as the continuity and boundedness of the linearized operator under reasonable assumptions using the maximal parabolic regularity theory.
In this paper, we describe the diffusive shallow water equation (DSW) and discuss a numerical strategy to solve it using the generalized-?? method as a method for temporal discretization. This method provides a good norm estimate of the error and guarantees an optimal convergence rate for the spatial discretization. We also discuss the effect of higher polynomial orders on the convergence rates, focusing on the nonlinear DSW problem. Our numerical experiments show that optional convergence rates can be obtained for polynomial orders 1 through 4.
We present a computationally efficient adaptive method for calculating the time evolution of the concentrations of chemical species in global 3-D models of atmospheric chemistry. Our strategy consists of partitioning the computational domain into fast and slow regions for each chemical species at every time step. In each grid box, we group the fast species and solve for their concentration in a coupled fashion. Concentrations of the slow species are calculated using a simple semi-implicit formula. Separation of species between fast and slow is done on the fly based on their local production and loss rates. This allows for example to exclude short-lived volatile organic compounds (VOCs) and their oxidation products from chemical calculations in the remote troposphere where their concentrations are negligible, letting the simulation determine the exclusion domain and allowing species to drop out individually from the coupled chemical calculation as their production/loss rates decline. We applied our method to a 1-year simulation of global tropospheric ozone-NOx-VOC-aerosol chemistry using the GEOS-Chem model. Results show a 50% improvement in computational performance for the chemical solver, with no significant added error.
Estimation of small-area population counts in an intercensal year and in a future year is a challenging task. This paper presents preliminary results in the development of a geographic-knowledge-guided cellular automata (CA) for modelling growth in small geographic areas. Geographic knowledge contains rules dictating growth patterns that typically cannot be captured by a traditional CA model. Nighttime stable light images and census population counts in censal years are used to determine base-year population counts in each cell in the CA model, and these estimated base-year population counts are used to manually calibrate the model. We use census data in 1990 and 2000 in El Paso County of Texas as the base-year population data, develop a set of rules based on specific urban-growth situations in El Paso and use the model to estimate population counts in block groups in a future year in the study area. Preliminary results in El Paso County suggest that the model has the potential to produce reasonably accurate population counts in sub-county areas in a future year. Future work will include the development of computational procedures that can be used to automate the calibration of the CA model.
In this paper, we study a local discontinuous Galerkin (LDG) method to approximate solutions of a doubly nonlinear diffusion equation, known in the literature as the diffusive wave approximation of the shallow water equations (DSW). This equation arises in shallow water flow models when special assumptions are used to simplify the shallow water equations and contains as particular cases: the Porous Medium equation and the parabolic p-Laplacian. Continuous in time a priori error estimates are established between the approximate solutions obtained using the proposed LDG method and weak solutions to the DSW equation under physically consistent assumptions. The results of numerical experiments in 2D are presented to verify the numerical accuracy of the method, and to show the qualitative properties of water flow captured by the DSW equation, when used as a model to simulate an idealized dam break problem with vegetation.
In this paper, we study the properties of approximate solutions to a doubly nonlinear and degenerate diffusion equation, known in the literature as the diffusive wave approximation of the shallow water equations (DSW), using a numerical approach based on the Galerkin finite element method. This equation arises in shallow water flow models when special assumptions are used to simplify the shallow water equations and contains as particular cases the porous medium equation and the p-Laplacian. Diverse numerical schemes have been implemented to approximately solve the DSW equation and have been successfully applied as suitable models to simulate overland flow and water flow in vegetated areas such as wetlands; yet, no formal mathematical analysis has been carried out in order to study the properties of approximate solutions. In this study, we propose a numerical approach as a means to understand some properties of solutions to the DSW equation and, thus, to provide conditions for which the use of the DSW equation may be inappropriate from both the physical and the mathematical points of view, within the context of shallow water modeling. For analysis purposes, we propose a numerical method based on the Galerkin method and we obtain a priori error estimates between the approximate solutions and weak solutions to the DSW equation under physically consistent assumptions. We also present some numerical experiments that provide relevant information about the accuracy of the proposed numerical method to solve the DSW equation and the applicability of the DSW equation as a model to simulate observed quantities in an experimental setting.
In this dissertation, the quantitative and qualitative aspects of modeling shallow water flow driven mainly by gravitational forces and dominated by shear stress, using an effective equation often referred to in the literature as the diffusive wave approximation of the shallow water equations (DSW) are presented. These flow conditions arise for example in overland flow and water flow in vegetated areas such as wetlands. The DSWequation arises in shallow water flow models when special assumptions are used to simplify the shallow water equations and contains as particular cases: the Porous Medium equation and the time evolution of the p-Laplacian. It has been successfully applied as a suitable model to simulate overland flow and water flow in vegetated areas such as wetlands; yet, no formal mathematical analysis has been carried out addressing, for example, conditions for which weak solutions may exist, and conditions for which a numerical scheme can be successful in approximating them. This thesis represents a first step in that direction. The outline of the thesis is as follows. First, a survey of relevant results coming from the studies of doubly nonlinear diffusion equations that can be applied to the DSWequation when topographic effects are ignored, is presented. Furthermore, an original proof of existence of weak solutions using constructive techniques that directly lead to the implementation of numerical algorithms to obtain approximate solutions is shown. Some regularity results about weak solutions are presented as well. Second, a numerical approach is proposed as a means to understand some properties of solutions to the DSW equation, when topographic effects are considered, and conditions for which the continuous and discontinuous Galerkin methods will succeed in approximating these weak solutions are established.
We discuss the use of time adaptivity applied to the one dimensional diffusive wave approximation to the shallow water equations. A simple and computationally economical error estimator is discussed which enables time-step size adaptivity. This robust adaptive time discretization corrects the initial time step size to achieve a user specified bound on the discretization error and allows time step size variations of several orders of magnitude. In particular, in the one dimensional results presented in this work feature a change of four orders of magnitudes for the time step over the entire simulation.
