Modeling the Short-Term Effect of Traffic and Meteorology on Air Pollution in Turin with Generalized Additive Models

Vehicular traffic plays an important role in atmospheric pollution and can be used as one of the key predictors in air-quality forecasting models. The models that can account for the role of traffic are especially valuable in urban areas, where high pollutant concentrations are often observed during particular times of day (rush hour) and year (winter). In this paper, we develop a generalized additive models approach to analyze the behavior of concentrations of nitrogen dioxide (NO2), and particulate matter (PM10), collected at the environmental monitoring stations distributed throughout the city of Turin, Italy, from December 2003 to April 2005. We describe nonlinear relationships between predictors and pollutants, that are adjusted for unobserved time-varying confounders. We examine several functional forms for the traffic variable and find that a simple form can often provide adequate modeling power. Our analysis shows that there is a saturation effect of traffic on NO2, while such saturation is less evident in models linking traffic to PM10behavior, having adjusted for meteorological covariates. Moreover, we consider the proposed models separately by seasons and highlight similarities and differences in the predictors' partial effects. Finally, we show how forecasting can help in evaluating traffic regulation policies

A Note on Species Richness and the Variance of Epidemic Severity

The commonly observed negative correlation between the number of species in an ecological community and disease risk, typically referred to as "the dilution effect", has received a substantial amount of attention over the past decade. Attempts to test this relationship experimentally have revealed that, in addition to the mean disease risk decreasing with species number, so too does the variance of disease risk. This is referred to as the "variance reduction effect", and has received relatively little attention in the disease-diversity literature. Here, we set out to clarify and quantify some of these relationships in an idealized model of a randomly assembled multi-species community undergoing an epidemic. We specifically investigate the variance of the community disease reproductive ratio, a multi-species extension of the basic reproductive ratio R_0, for a family of random-parameter meta-community SIR models, and show how the variance of community $R_0$ varies depending on whether transmission is density or frequency-dependent. We finally outline areas of further research on how changes in variance affect transmission dynamics in other systems

Population-level differences in disease transmission: A Bayesian analysis of multiple smallpox epidemics

Estimates of a disease\u27s basic reproductive rate R0 play a central role in understanding outbreaks and planning intervention strategies. In many calculations of R0, a simplifying assumption is that different host populations have effectively identical transmission rates. This assumption can lead to an underestimate of the overall uncertainty associated with R0, which, due to the non-linearity of epidemic processes, may result in a mis-estimate of epidemic intensity and miscalculated expenditures associated with public-health interventions. In this paper, we utilize a Bayesian method for quantifying the overall uncertainty arising from differences in population-specific basic reproductive rates. Using this method, we fit spatial and non-spatial susceptible-exposed-infected-recovered (SEIR) models to a series of 13 smallpox outbreaks. Five outbreaks occurred in populations that had been previously exposed to smallpox, while the remaining eight occurred in Native-American populations that were naïve to the disease at the time. The Native-American outbreaks were close in a spatial and temporal sense. Using Bayesian Information Criterion (BIC), we show that the best model includes population-specific R0 values. These differences in R0 values may, in part, be due to differences in genetic background, social structure, or food and water availability. As a result of these inter-population differences, the overall uncertainty associated with the population average value of smallpox R0 is larger, a finding that can have important consequences for controlling epidemics. In general, Bayesian hierarchical models are able to properly account for the uncertainty associated with multiple epidemics, provide a clearer understanding of variability in epidemic dynamics, and yield a better assessment of the range of potential risks and consequences that decision makers face. © 2013 Elsevier B.V

Direct Estimation of Parameters in ODE Models Using WENDy: Weak-form Estimation of Nonlinear Dynamics

We introduce the Weak-form Estimation of Nonlinear Dynamics (WENDy) method for estimating model parameters for non-linear systems of ODEs. Without relying on any numerical differential equation solvers, WENDy computes accurate estimates and is robust to large (biologically relevant) levels of measurement noise. For low dimensional systems with modest amounts of data, WENDy is competitive with conventional forward solver-based nonlinear least squares methods in terms of speed and accuracy. For both higher dimensional systems and stiff systems, WENDy is typically both faster (often by orders of magnitude) and more accurate than forward solver-based approaches. The core mathematical idea involves an efficient conversion of the strong form representation of a model to its weak form, and then solving a regression problem to perform parameter inference. The core statistical idea rests on the Errors-In-Variables framework, which necessitates the use of the iteratively reweighted least squares algorithm. Further improvements are obtained by using orthonormal test functions, created from a set of C-infinity bump functions of varying support sizes. We demonstrate the high robustness and computational efficiency by applying WENDy to estimate parameters in some common models from population biology, neuroscience, and biochemistry, including logistic growth, Lotka-Volterra, FitzHugh-Nagumo, Hindmarsh-Rose, and a Protein Transduction Benchmark model. Software and code for reproducing the examples is available at (https://github.com/MathBioCU/WENDy).Comment: 28 pages, 16 figure