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

Uncertainty in predictions of disease spread and public health responses to bioterrorism and emerging diseases

Concerns over bioterrorism and emerging diseases have led to the widespread use of epidemic models for evaluating public health strategies. Partly because epidemic models often capture the dynamics of prior epidemics remarkably well, little attention has been paid to how uncertainty in parameter estimates might affect model predictions. To understand such effects, we used Bayesian statistics to rigorously estimate the uncertainty in the parameters of an epidemic model, focusing on smallpox bioterrorism. We then used a vaccination model to translate the uncertainty in the model parameters into uncertainty in which of two vaccination strategies would provide a better response to bioterrorism, mass vaccination, or vaccination of social contacts, so-called trace vaccination. Our results show that the uncertainty in the model parameters is remarkably high and that this uncertainty has important implications for vaccination strategies. For example, under one plausible scenario, the most likely outcome is that mass vaccination would save ≈100,000 more lives than trace vaccination. Because of the high uncertainty in the parameters, however, there is also a substantial probability that mass vaccination would save 200,000 or more lives than trace vaccination. In addition to providing the best response to the most likely outcome, mass vaccination thus has the advantage of preventing outcomes that are only slightly less likely but that are substantially more horrific. Rigorous estimates of uncertainty thus can reveal hidden advantages of public health strategies, suggesting that formal uncertainty estimation should play a key role in planning for epidemics. © 2006 by The National Academy of Sciences of the USA

Who Underreports Smoking on Birth Records: A Monte Carlo Predictive Model with Validation

Research has shown that self-reports of smoking during pregnancy may underestimate true prevalence. However, little is known about which populations have higher rates of underreporting. Availability of more accurate measures of smoking during pregnancy could greatly enhance the usefulness of existing studies on the effects of maternal smoking offspring, especially in those populations where underreporting may lead to underestimation of the impact of smoking during pregnancy.In this paper, we develop a statistical Monte Carlo model to estimate patterns of underreporting of smoking during pregnancy, and apply it to analyze the smoking self-report data from birth certificates in the state of Massachusetts. Our results illustrate non-uniform patterns of underreporting of smoking during pregnancy among different populations. Estimates of likely underreporting of smoking during pregnancy were highest among mothers who were college-educated, married, aged 30 years or older, employed full-time, and planning to breastfeed. The model's findings are validated and compared to an existing underreporting adjustment approach in the Maternal and Infant Smoking Study of East Boston (MISSEB).The validation results show that when biological assays are not available, the Monte Carlo method proposed can provide a more accurate estimate of the smoking status during pregnancy than self-reports alone. Such methods hold promise for providing a better assessment of the impact of smoking during pregnancy

Internet Queries and Methicillin-Resistant Staphylococcus aureus Surveillance

The Internet is a common source of medical information and has created novel surveillance opportunities. We assessed the potential for Internet-based surveillance of methicillin-resistant Staphylococcus aureus and examined the extent to which it reflects trends in hospitalizations and news coverage. Google queries were a useful predictor of hospitalizations for methicillin-resistant S. aureus infections

An empirical test of the role of small-scale transmission in large-scale disease dynamics

A key assumption of epidemiological models is that population-scale disease spread is driven by close contact between hosts and pathogens. At larger scales, however, mechanisms such as spatial structure in host and pathogen populations and environmental heterogeneity could alter disease spread. The assumption that small-scale transmission mechanisms are sufficient to explain large-scale infection rates, however, is rarely tested. Here, we provide a rigorous test using an insect-baculovirus system. We fit a mathematical model to data from forest-wide epizootics while constraining the model parameters with data from branch-scale experiments, a difference in spatial scale of four orders of magnitude. This experimentally constrained model fits the epizootic data well, supporting the role of small-scale transmission, but variability is high. We then compare this model's performance to an unconstrained model that ignores the experimental data, which serves as a proxy for models with additional mechanisms. The unconstrained model has a superior fit, revealing a higher transmission rate across forests compared with branch-scale estimates. Our study suggests that small-scale transmission is insufficient to explain baculovirus epizootics. Further research is needed to identify the mechanisms that contribute to disease spread across large spatial scales, and synthesizing models and multiscale data are key to understanding these dynamics.</p