Prediction of the Change Rate of Tumor Cells, Healthy Host Cells, and Effector Immune Cells in a Three-Dimensional Cancer Model using Extended Kalman Filter - Fitriyati, Nina; Faizah, Salma Abidah; Sutanto, Taufik Edy (Jambura Journal of Biomathematics (JJBM), 2024)
In this study, we develop and implement the Extended Kalman Filter (EKF) to forecast the rate of change in tumor cells, healthy host cells, and effector immune cells within the Itik-Banks model. This novel application of EKF in cancer dynamics modeling aims to provide precise real-time estimations of cellular interactions, especially in constructing a new state space representation from the Itik-Banks model. We use a first-order Taylor series to linearize the model. The numerical simulations were performed to analyze the accuracy of this new state space with data from William Gilpin's GitHub repository. The results show that the EKF predictions strongly align with actual data, i.e., in the prior and posterior steps for tumor and healthy host cells, there is a strong agreement between the predictions and the actual data. The EKF captures the oscillatory nature of the tumor and healthy host cell population well. The peaks and troughs of the predictions align closely with the actual data, indicating the EKF's effectiveness in modeling the dynamic behavior of the tumor and healthy host cells. However, for effector immune cells, the oscillatory nature of the data in these cells gives rise to slight deviations. This represents a significant challenge in the future for updating the state space representations. Despite minor discrepancies, the EKF demonstrates a strong performance in both the training and testing data, with the posterior step estimates significantly improving the prior step accuracy. This study emphasizes the importance of data availability for accurate predictions, noting a symmetric Mean Absolute Percentage Error (sMAPE) of 35.92% when data is unavailable. Prompt correction with new data is essential to maintain accuracy. This research underscores the EKF's potential for real-time monitoring and prediction in complex biological systems.