This paper deals with a model for prolactin (PRL) secretion under the effects of dopamine (DA) and the thyrotropin-releasing (TRH) hormone. The model consists of a system of nonlinear delay differential equations, in which the time delay is taken into account in the secretion rate of DA due to the feedback action of PRL at the hypotalamic level.
In order to establish the existence of periodic solutions to the model, the paper studies the existence of a Hopf bifurcation, considering the delay as a parameter. Using standard tools to analyze the roots of a transcendental characteristic equation, sufficient conditions to asssure the existence of periodic solutions are stated, resembling the pulsatile (PRL) secretion pattern which has been observed clinically. In addition, some numerical simulations of the model show the possibility of an irregular pattern of PRL secretion, which has been observed clinically in patients with both microprolactinoma and macroprolactinoma.