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Applied Longitudinal Data Analysis Modeling Change And Event Occurrence

International journal of infectious diseases : IJID : official publication of the International Society for Infectious Diseases.

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Elements Of Mathematical Ecology

Excessive alcohol use cost the U.S. $223.5 billion in 2006. Given economic shifts in the U.S. since 2006, more-current estimates are needed to help inform the planning of prevention strategies.

2010 National and State Costs of Excessive Alcohol Consumption

Ocular blood flow as a clinical observation: Value, limitations and data analysis

Because of limited data, much remains uncertain about parameters related to transmission dynamics of Zika virus (ZIKV). Estimating a large number of parameters from the limited information in data may not provide useful knowledge about the ZIKV. Here, we developed a method that utilizes a mathematical model of ZIKV dynamics and the complex-step derivative approximation technique to identify parameters that can be estimated from the available data. Applying our method to epidemic data from the ZIKV outbreaks in French Polynesia and Yap Island, we identified the parameters that can be estimated from these island data. Our results suggest that the parameters that can be estimated from a given data set, as well as the estimated values of those parameters, vary from Island to Island. Our method allowed us to estimate some ZIKV-related parameters with reasonable confidence intervals. We also computed the basic reproduction number to be from 2.03 to 3.20 across islands. Furthermore, using our model, we evaluated potential prevention strategies and found that peak prevalence can be reduced to nearly 10% by reducing mosquito-to-human contact by at least 60% or increasing mosquito death by at least a factor of three of the base case. With these preventions, the final outbreak-size is predicted to be negligible, thereby successfully controlling ZIKV epidemics.

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Modeling Zika Virus Transmission Dynamics: Parameter Estimates, Disease Characteristics, and Prevention.

Sensitivity analysis in poro-elastic and poro-visco-elastic models with respect to boundary data

In this report, we use the complex-step derivative approximation technique to compute sensitivities for delay differential equations (DDEs) with non-smooth (discontinuous and even distributional) history functions. We compare the results with exact derivatives and with those computed using the classical sensitivity equations whenever possible. Our results demonstrate that the implementation of the complex-step method using the method of steps and the Matlab solver dde23 provides a very good approximation of sensitivities as long as discontinuities in the initial data do not cause loss of smoothness in the solution: that is, even when the underlying smoothness with respect to the initial data for the Cauchy-Riemann derivation of the the method does not hold. We conclude with remarks on our findings regarding the complex-step method for computing sensitivities for simpler ordinary differential equation systems in the event of lack of smoothness with respect to parameters.

Sensitivity via the complex-step method for delay differential equations with non-smooth initial data

Dynamic Modeling of Problem Drinkers Undergoing Behavioral Treatment.

Poro-elastic systems have been used extensively in modeling fluid flow in porous media in petroleum and earthquake engineering. Nowadays, they are frequently used to model fluid flow through biological tissues, cartilages, and bones. In these biological applications, the fluid-solid mixture problems, which may also incorporate structural viscosity, are considered on bounded domains with appropriate non-homogeneous boundary conditions. The recent work in [ 12 ] provided a theoretical and numerical analysis of nonlinear poro-elastic and poro-viscoelastic models on bounded domains with mixed boundary conditions, focusing on the role of visco-elasticity in the material. Their results show that higher time regularity of the sources is needed to guarantee bounded solution when visco-elasticity is not present. Inspired by their results, we have recently performed local sensitivity analysis on the solutions of these fluid-solid mixture problems with respect to the boundary source of traction associated with the elastic structure [ 3 ]. Our results show that the solution is more sensitive to boundary datum in the purely elastic case than when visco-elasticity is present in the solid matrix. In this article, we further extend this work in order to include local sensitivities of the solution of the coupled system to the boundary conditions imposed on the Darcy velocity. Sensitivity analysis is the first step in identifying important parameters to control or use as control terms in these poro-elastic and poro-visco-elastic models, which is our ultimate goal.

Kidist Bekele-Maxwell

Papers

Modeling Zika Virus Transmission Dynamics: Parameter Estimates, Disease Characteristics, and Prevention.

Sensitivity analysis in poro-elastic and poro-visco-elastic models with respect to boundary data

Sensitivity via the complex-step method for delay differential equations with non-smooth initial data

Dynamic Modeling of Problem Drinkers Undergoing Behavioral Treatment.

Local sensitivity via the complex-step derivative approximation for 1D Poro-Elastic and Poro-Visco-Elastic models