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BACKGROUND: The World Health Organization declared the ongoing Zika virus (ZIKV) epidemic in the Americas a Public Health Emergency of International Concern on February 1, 2016. ZIKV disease in humans is characterized by a "dengue-like" syndrome including febrile illness and rash. However, ZIKV infection in early pregnancy has been associated with severe birth defects, including microcephaly and other developmental issues. Mechanistic models of disease transmission can be used to forecast trajectories and likely disease burden but are currently hampered by substantial uncertainty on the epidemiology of the disease (e.g., the role of asymptomatic transmission, generation interval, incubation period, and key drivers). When insight is limited, phenomenological models provide a starting point for estimation of key transmission parameters, such as the reproduction number, and forecasts of epidemic impact. METHODS: We obtained daily counts of suspected Zika cases by date of symptoms onset from the Secretary of Health of Antioquia, Colombia during January-April 2016. We calibrated the generalized Richards model, a phenomenological model that accommodates a variety of early exponential and sub-exponential growth kinetics, against the early epidemic trajectory and generated predictions of epidemic size. The reproduction number was estimated by applying the renewal equation to incident cases simulated from the fitted generalized-growth model and assuming gamma or exponentially-distributed generation intervals derived from the literature. We estimated the reproduction number for an increasing duration of the epidemic growth phase. RESULTS: The reproduction number rapidly declined from 10.3 (95% CI: 8.3, 12.4) in the first disease generation to 2.2 (95% CI: 1.9, 2.8) in the second disease generation, assuming a gamma-distributed generation interval with the mean of 14 days and standard deviation of 2 days. The generalized-Richards model outperformed the logistic growth model an

Background:Assessing the mortality impact of the 2009 influenza A H1N1 virus (H1N1pdm09) is essential for optimizing public health responses to future pandemics. The World Health Organization reported 18,631 laboratory-confirmed pandemic deaths, but the total pandemic mortality burden was substantially higher. We estimated the 2009 pandemic mortality burden through statistical modeling of mortality data from multiple countries.Methods and Findings:We obtained weekly virology and underlying cause-of-death mortality time series for 2005-2009 for 20 countries covering ∼35% of the world population. We applied a multivariate linear regression model to estimate pandemic respiratory mortality in each collaborating country. We then used these results plus ten country indicators in a multiple imputation model to project the mortality burden in all world countries. Between 123,000 and 203,000 pandemic respiratory deaths were estimated globally for the last 9 mo of 2009. The majority (62%-85%) were attributed to persons under 65 y of age. We observed a striking regional heterogeneity, with almost 20-fold higher mortality in some countries in the Americas than in Europe. The model attributed 148,000-249,000 respiratory deaths to influenza in an average pre-pandemic season, with only 19% in persons <65 y. Limitations include lack of representation of low-income countries among single-country estimates and an inability to study subsequent pandemic waves (2010-2012).Conclusions:We estimate that 2009 global pandemic respiratory mortality was ∼10-fold higher than the World Health Organization's laboratory-confirmed mortality count. Although the pandemic mortality estimate was similar in magnitude to that of seasonal influenza, a marked shift toward mortality among persons <65 y of age occurred, so that many more life-years were lost. The burden varied greatly among countries, corroborating early reports of far greater pandemic severity in the Americas than in Australia, New Zealand

A method for estimating parameters in dynamic stochastic (Markov Chain) models based on Kurtz's limit theory coupled with inverse problem methods developed for deterministic dynamical systems is proposed and illustrated in the context of disease dynamics. This methodology relies on finding an approximate large-population behavior of an appropriate scaled stochastic system. This approach leads to a deterministic approximation obtained as solutions of rate equations (ordinary differential equations) in terms of the large sample size average over sample paths or trajectories (limits of pure jump Markov processes). Using the resulting deterministic model we select parameter subset combinations that can be estimated using an ordinary-least- squares (OLS) or generalized-least-squares (GLS) inverse problem formulation with a given data set. The selection is based on two criteria of the sensitivity matrix: the degree of sensitivity measure in the form of its condition number and the degree of uncertainty measured in the form of its parameter selection score. We illustrate the ideas with a stochastic model for the transmission of vancomycin-resistant enterococcus (VRE) in hospitals and VRE surveillance data from an oncology unit., Prepared in cooperation with Arizona State Univ., School of Human Evolution and Social Change, Tempa, AZ.

Surveillance data from an oncology hospital unit on Vancomycin-resistant Enterococcus (VRE), one of the most prevalent and dangerous pathogens involved in hospital infections, is used to motivate possibilities of modeling nosocomial infection dynamics. This is done in the context of hospital monitoring and isolation procedures as a prelude to the evaluation and improved design of control measures. A discrete event delay differential equation model in conjunction with statistical computational methods is formulated to estimate key population-level nosocomial transmission parameters and isolation procedures. This framework is used to test the surveillance data's usefulness in model validation. In the process of model calibration we discovered significant irregularities in the available surveillance data; these irregularities are most likely the result of the data observational recording process as well as those in the isolation procedures. Efforts to fit data within our highly flexible dynamic-modeling framework suggest that clinical-trial level surveillance data is needed if one is to successfully develop quantitative models for disease transmission and intervention. It is concluded that typical cold data sets typically encountered in biological/sociological quantitative modeling efforts may be inadequate for support of serious model development., Prepared in cooperation with Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC.