The cardiovascular system may be investigated by observing fluctuations in the heart rate, blood pressure and rate of respiration. Its time evolution is governed by the baroreflex control mechanism, where the sympathetic and vagal nerves compete to increase and decrease the heart rate respectively. A nonlinear delay-differential equation model is constructed to describe this control mechanism and to explore the interactions between the heart rate and blood pressure. In this model, a time delay gives rise to the oscillations in the blood pressure known as Mayer waves. The model maintains an intrinsically stable heart rate in the absence of nervous control, and features baroreflex influence on both heart rate and peripheral resistance. The effect of respiratory sinus arrhythmia (RSA) is introduced using a sinusoidal driving component. Clinical recordings obtained by carefully controlling the rate and depth of respiration are used to test the suitability of the model for representing the complicated physiology of the cardiovascular system. The model is shown to be able to reproduce many of the empirical characteristics observed in these biomedical signals, including RSA, Mayer waves and synchronization. Key physiological parameters in the model, including the time delay and levels of sympathetic and vagal activity, could provide useful diagnostic information about the state of the cardiovascular system.