Stability Analysis of a Mathematical Model of Hormonal Contraception

Combination oral contraceptives (COCs), containing a combination of synthetic progestin and estrogen, have become a leading form of contraception in the United States. The pill is taken cyclically, meaning it is taken regularly during a certain “on” period, followed by a shorter “off” period during which menstruation occurs. In order for the pill to be effective, it must be taken daily during the “on” period and it is recommended that it be taken around the same time every day. This requirement poses a challenge to many users and can result in unwanted pregnancies. We explore the stability of the contraceptive state achieved by hormonal birth control using a mechanistic mathematical model of the menstrual cycle. Specifically, we build off a model by Wright and colleagues, in which the authors model concentrations of exogenous progestin and estrogen as a constant. We include the dynamics of the on/off dosing of COC's by introducing a time-dependent function for exogenous estrogen and progestin and investigate the stability of the model in response to changes in exogenous hormone dosing. Accurately modeling COC dosing could provide insight into when a contraceptive state has been lost due to inconsistency or changes in hormonal birth control use.