James F. Selgrade

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Increasing concerns that environmental contaminants may disrupt the endocrine system require development of mathematical tools to predict the potential for such compounds to significantly alter human endocrine function. The endocrine system is largely self-regulating, compensating for moderate changes in dietary phytoestrogens (e.g., in soy products) and(More)
This study presents a strategy for developing a mathematical model describing the concentrations of five hormones important for regulation and maintenance of the menstrual cycle. Models which correctly predict the serum levels of ovarian and pituitary hormones may assist the experimentalist by indicating directions of investigation. In addition, model(More)
A system of non-linear difference equations is used to model the effects of density-dependent selection and migration in a population characterized by two alleles at a single gene locus. Results for the existence and stability of polymorphic equilibria are established. Properties for a genetically important class of equilibria associated with complete(More)
In this study, a mathematical model is developed for the production of the ovarian hormones (estradiol, progesterone, and inhibin) with input functions which represent blood levels of the gonadotropin hormones (luteinizing hormone and follicle stimulating hormone). A 9-dimensional system of linear, nonautonomous, ordinary differential equations tracks the(More)
This study presents a nonlinear system of delay differential equations to model the concentrations of five hormones important for regulation and maintenance of the menstrual cycle. Linear model components for the ovaries and pituitary were previously analyzed and reported separately. Results for the integrated model are now presented here. This model(More)
This study presents a 13-dimensional system of delayed differential equations which predicts serum concentrations of five hormones important for regulation of the menstrual cycle. Parameters for the system are fit to two different data sets for normally cycling women. For these best fit parameter sets, model simulations agree well with the two different(More)
This work discusses the effects of periodic forcing on attracting cycles and more complicated attractors for autonomous systems of nonlinear difference equations. Results indicate that an attractor for a periodically forced dynamical system may inherit structure from an attractor of the autonomous (unforced) system and also from the periodicity of the(More)
This study considers a general class of twodimensional, discrete population models where each per capita transition function (fitness) depends on a linear combination of the densities of the interacting populations. The fitness functions are either monotone decreasing functions (pioneer fitnesses) or one-humped functions (climax fitnesses). Conditions are(More)
Polycystic ovary syndrome (PCOS), a common cause of infertility in women, is often accompanied by abnormal reproductive and metabolic hormone levels. Specifically, androgens such as testosterone are elevated in many PCOS women, and the syndrome itself is frequently associated with insulin resistance, which leads to hyperinsulinemia, i.e., elevated insulin.(More)