I am currently a Professor in the Department of Mathematics – Physics at University of Puerto Rico in Cayey. I have a Ph.D. in Applied Mathematics for the Life and Social Sciences from Arizona State University. My research is related to mathematical models of life events such as the dynamic of metapopulation models of the spread of diseases. I am currently working on models of neuro-endocrinology systems.
The topics of mathematical population and biological disease models interest me because it is a way to apply mathematics in real life situations that are important for our society, to protect the population from an epidemic, and to help governments make wise decisions to eradicate (or mitigate the effect of) diseases. My Ph.D.~dissertation research explores the different scenarios of the novel AH1N1 influenza virus. As part of my dissertation, my current work further examines the influence of different factors considering the randomness of events by adding stochastic processes to meta-population models. I present three different approaches to compare different stochastic methods by considering discrete and continuous time. For the continuous time stochastic modeling approach we consider the continuous-time Markov chain process using forward Kolmogorov equations while for the discrete time stochastic modeling we consider the stochastic differential equations using Wiener’s increment and Poisson point increments and for the discrete time stochastic modeling we consider the discrete-time Markov chain process. These three stochastic modeling approaches are presented in a two city epidemic model using, as a base, our deterministic model.
To expand my research work I intend to explore on neuro-endocrine system modeling of hormone interactions in the endocrine system. My interest in this topic is quite personal and I want to understand the mechanisms that affect the metabolism and reproductive system in females particularly behind a syndrome called Polycystic Ovarian Syndrome (PCOS). In particular, I will want to focus on the relationship between insulin resistance and PCOS with a focus on the effectiveness of the regulation of the menstrual cycle using the drug Metformin (Glucophage) that accidentally was proven to help regulate the menstrual cycle by means of control the insulin resistance in patients with PCOS. (Personal communication with my endocrinologist and http://www.ovarian-cysts-pcos.com/glucophage-metformin-pcos.html). I believe my training and modeling experience in mathematical biology has prepared me to undertake such work and contribute in significant ways to the literature in these areas.