@article{banks_cintron-arias_kappel_2013, title={Parameter selection methods in inverse problem formulation}, volume={2064}, journal={Mathematical modeling and validation in physiology: applications to the cardiovascular and respiratory systems}, author={Banks, H. T. and Cintron-Arias, A. and Kappel, F.}, year={2013}, pages={43–73} }
 @article{banks_holm_wanner_cintron-arias_kepler_wetherington_2009, title={A mathematical model for the first-pass dynamics of antibiotics acting on the cardiovascular system}, volume={50}, ISSN={["1872-9479"]}, DOI={10.1016/j.mcm.2009.02.007}, abstractNote={We present a preliminary first-pass dynamic model for delivery of drug compounds to the lungs and heart. We use a compartmental mass balance approach to develop a system of nonlinear differential equations for mass accumulated in the heart as a result of intravenous injection. We discuss sensitivity analysis as well as methodology for minimizing mass in the heart while maximizing mass delivered to the lungs on a first circulatory pass.}, number={7-8}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Banks, H. T. and Holm, Kathleen and Wanner, Nathan C. and Cintron-Arias, Ariel and Kepler, Grace M. and Wetherington, Jeffrey D.}, year={2009}, month={Oct}, pages={959–974} }
 @article{cintron-arias_banks_capaldi_lloyd_2009, title={A sensitivity matrix based methodology for inverse problem formulation}, volume={17}, ISSN={["1569-3945"]}, DOI={10.1515/JIIP.2009.034}, abstractNote={Abstract We propose an algorithm to select parameter subset combinations that can be estimated using an ordinary least-squares (OLS) inverse problem formulation with a given data set. First, the algorithm selects the parameter combinations that correspond to sensitivity matrices with full rank. Second, the algorithm involves uncertainty quantification by using the inverse of the Fisher Information Matrix. Nominal values of parameters are used to construct synthetic data sets, and explore the effects of removing certain parameters from those to be estimated using OLS procedures. We quantify these effects in a score for a vector parameter defined using the norm of the vector of standard errors for components of estimates divided by the estimates. In some cases the method leads to reduction of the standard error for a parameter to less than 1% of the estimate.}, number={6}, journal={JOURNAL OF INVERSE AND ILL-POSED PROBLEMS}, author={Cintron-Arias, A. and Banks, H. T. and Capaldi, A. and Lloyd, A. L.}, year={2009}, month={Aug}, pages={545–564} }
 @article{cintron-arias_castillo-chavez_bettencourt_lloyd_banks_2009, title={THE ESTIMATION OF THE EFFECTIVE REPRODUCTIVE NUMBER FROM DISEASE OUTBREAK DATA}, volume={6}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2009.6.261}, abstractNote={We consider a single outbreak susceptible-infected-recovered (SIR) model and corresponding estimation procedures for the effective reproductive number R(t). We discuss the estimation of the underlying SIR parameters with a generalized least squares (GLS) estimation technique. We do this in the context of appropriate statistical models for the measurement process. We use asymptotic statistical theories to derive the mean and variance of the limiting (Gaussian) sampling distribution and to perform post statistical analysis of the inverse problems. We illustrate the ideas and pitfalls (e.g., large condition numbers on the corresponding Fisher information matrix) with both synthetic and influenza incidence data sets.}, number={2}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Cintron-Arias, Ariel and Castillo-Chavez, Carlos and Bettencourt, Luis M. A. and Lloyd, Alun L. and Banks, H. T.}, year={2009}, month={Apr}, pages={261–282} }