We develop a patient-specific dynamical system model from the time series data of the cancer patient’s metabolic panel taken during the period of cancer treatment and recovery. The model consists of a pair of stacked long short-term memory (LSTM) recurrent neural networks and a fully connected neural network in each unit. It is intended to be used by physicians to trace back and look forward at the patient’s metabolic indices, to identify potential adverse events, and to make short-term predictions. When the model is used in making short-term predictions, the relative error in every index is less than 10% in the L∞ norm and less than 6.3% in the L1 norm in the validation process. Once a master model is built, the patient-specific model can be calibrated through transfer learning. As an example, we obtain patient-specific models for four more cancer patients through transfer learning, which all exhibit reduced training time and a comparable level of accuracy. This study demonstrates that this modeling approach is reliable and can deliver clinically acceptable physiological models for tracking and forecasting patients’ metabolic indices.