Effects of Skin Thermoregulation Delay in a Dynamical Model of Heat Transfer in an Infant Incubator

Abstract

Infant incubators are lifelines for millions of premature and sick infants worldwide. This device regulates an appropriate environment, where temperature control holds utmost importance. Heat transfer in infant incubators was previously studied using ODE models that did not account for temperature fluctuations due to fat and skin thickness. Hence, a system of delay differential equations describing heat transfer in an infant incubator considering skin thermoregulation delay, which is reflected using a time-delay parameter, is proposed and analyzed in this paper. Initial results include the existence of a unique positive equilibrium describing the ideal temperatures of the infant’s core, skin, and the incubator’s air space. To investigate the effects of the skin thermoregulation delay on the dynamical behavior near the equilibrium, a local stability analysis was performed using the time delay as the main parameter. Conditions for the absolute stability of the equilibrium and occurrence of stability switches were derived. In the latter case, a locally asymptotically stable equilibrium can become unstable due to the occurrence of a Hopf bifurcation at a threshold value of the time-delay parameter. Numerical simulations reveal that the limit-cycle solutions born from the Hopf bifurcation can lead to extreme temperature fluctuations, catastrophic for the infant. To maintain the ideal temperatures, the aim is to have conditions where the equilibrium is either absolutely stable or the time-delay parameter is kept lower than the threshold value. This paper helps to better understand the dynamics of heat transfer in an infant incubator, which benefits premature and sick infants.