A Sensitivity Matrix Methodology for Inverse Problem Formulation

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

Dynamics of a Two-Dimensional Discrete-Time SIS Model

24 pages, 1 article*Dynamics of a Two-Dimensional Discrete-Time SIS Model* (Barrera, Jaime H.; Cintron-Arias, Ariel; Davidenko, Nicolas; Denogean, Lisa; Franco-Gonzalez, Saul R.) 24 page

Optimal Control of Drug Therapy in a Hepatitis B Model

Combination antiviral drug therapy improves the survival rates of patients chronically infected with hepatitis B virus by controlling viral replication and enhancing immune responses. Some of these drugs have side effects that make them unsuitable for long-term administration. To address the trade-off between the positive and negative effects of the combination therapy, we investigated an optimal control problem for a delay differential equation model of immune responses to hepatitis virus B infection. Our optimal control problem investigates the interplay between virological and immunomodulatory effects of therapy, the control of viremia and the administration of the minimal dosage over a short period of time. Our numerical results show that the high drug levels that induce immune modulation rather than suppression of virological factors are essential for the clearance of hepatitis B virus

Epidemiology as Related to Phylogenetic Distances of the Influenza Virus

The evolution of the influenza virus is characterized by continual changes to its surface structures due to antigenic drift and antigenic shift. In response, the host immune system must alter antibodies in response to the ever-changing virus allowing for the persistence of influenza in a host population. The spread of related strains to a susceptible population with regard to their phylogenetic distance from a parental strain during a season is examined, as well as the dynamics of the immune response within a single host. Very little work has been done to integrate phylogenetic analysis of evolution with the epidemiological spread of the influenza virus. In this study, an attempt is made to couple these two scales by using infection rates that are defined as functions of phylogenetic distances between strains. Competition between strains is focused on and strain prevalence for outbreaks during several seasons (2000-2004, inclusive) is examined at various levels: global, regional, and for New York City. Coexistence is found to only be possible between very similar strains, otherwise competitive exclusion or extinction of all strains occur. Stochastic simulations at the cellular level indicate that the immune system is most effective when the virus has little variability, so the rapid mutation of influenza is an effective strategy in evading the immune system. Similar simulations for the population level show that a strain\u27s prevalence depends largely on the level of change in antigenic structure is produced by amino acid mutations

A Stochastic Approach for Modeling Treatment and Diagnosis of Attention Deficit Disorder

21 pages, 1 article*A Stochastic Approach for Modeling Treatment and Diagnosis of Attention Deficit Disorder* (Acevedo-Estefania, Carlos; Torre, Carlos; Cintron-Arias, Ariel; Hernandez-Suarez, Carlos; Nshinyabakobeje, Sophonie) 21 page

Estimation of the Population Vaccination Effectiveness Using Urn Models

17 pages, 1 article*Estimation of the Population Vaccination Effectiveness Using Urn Models* (Cintron-Arias, Ariel; Hernandez-Suarez, Carlos; Barrera-Rodriguez, Carlos; Espinoza-Limon, Angelina; Vargas-Bracamontes, Dulce) 17 page