The emergence and progression of multiple chronic conditions (MCC) over time often form a dynamic network that depends on patient's modifiable risk factors and their interaction with non-modifiable risk factors and existing conditions. Continuous time Bayesian networks (CTBNs) are effective methods for modeling the complex network of MCC relationships over time. However, CTBNs are not able to effectively formulate the dynamic impact of patient's modifiable risk factors on the emergence and progression of MCC. Considering a functional CTBN (FCTBN) to represent the underlying structure of the MCC relationships with respect to individuals' risk factors and existing conditions, we propose a nonlinear state-space model based on Extended Kalman filter (EKF) to capture the dynamics of the patients' modifiable risk factors and existing conditions on the MCC evolution over time. We also develop a tensor control chart to dynamically monitor the effect of changes in the modifiable risk factors of individual patients on the risk of new chronic conditions emergence. We validate the proposed approach based on a combination of simulation and real data from a dataset of 385 patients from Cameron County Hispanic Cohort (CCHC) over multiple years. The dataset examines the emergence of 5 chronic conditions (Diabetes, Obesity, Cognitive Impairment, Hyperlipidemia, and Hypertension) based on 4 modifiable risk factors representing lifestyle behaviors (Diet, Exercise, Smoking Habit, and Drinking Habit) and 3 non-modifiable risk factors, including demographic information (Age, Gender, Education). The results demonstrate the effectiveness of the proposed methodology for dynamic prediction and monitoring of the risk of MCC emergence in individual patients.