Obstructive sleep apnea (OSA) is a serious sleep disorder affecting millions of people worldwide. There is a great need to develop an efficient, low-cost OSA detection method. Traditional OSA detection methods are purely data-driven and hence their detection performance greatly depends on the quality and quantity of the sensor data. Several mathematical models of the human cardiorespiratory system exist which can generate different physiological signals that are hard to measure using current sensor technology. In this paper, we propose a new framework for OSA detection in which we fuse the sensor data with the physiological signal data from the cardiorespiratory system models. Multivariate Gaussian processes (GPs) are used to capture and model the physiological signal variations among different individuals. We define the multivariate GP covariance function using the sum of separable kernel functions form and estimate the corresponding hyperparameters by maximizing the GP marginal likelihood function. We detect OSA using the heart rate signal on a window-by-window basis using a likelihood ratio test. We conduct several experiments on both simulated and real data to show the effectiveness of the proposed OSA detection framework. We also compare with other purely data-driven OSA detection methods to demonstrate the advantage of the proposed OSA detection fusion framework.