James F. Selgrade

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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 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 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)
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)
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)
A model for hormonal control of the menstrual cycle with 13 ordinary differential equations and 41 parameters is presented. Important changes in model behavior result from variations in two of the most sensitive parameters. One parameter represents the level of estradiol sufficient for significant synthesis of luteinizing hormone, which causes ovulation. By(More)
A system of 13 ordinary differential equations with 42 parameters is presented to model hormonal regulation of the menstrual cycle. For an excellent fit to clinical data, the model requires a 36 h time delay for the effect of inhibin on the synthesis of follicle stimulating hormone. Biological and mathematical reasons for this delay are discussed.(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 16 non-linear, delay differential equations with 66 parameters is developed to model hormonal regulation of the menstrual cycle of a woman from age 20 to 51. This mechanistic model predicts changes in follicle numbers and reproductive hormones that naturally occur over that time span. In particular, the model illustrates the decline in the pool(More)