Exploration of Hepatitis B Virus Infection Dynamics through Physics-Informed Deep Learning Approach.

Accurate forecasting of viral disease outbreaks is crucial for guiding public health responses and preventing widespread loss of life. Recently, Physics-Informed Neural Networks (PINNs) have emerged as a promising framework for capturing viral infection dynamics and predicting their future progression. Standard PINNs are effective in simulating disease dynamics through forward modeling approach; however, they often face challenges in estimating key biological parameters from sparse or noisy data in inverse problems. To overcome these limitations, a recent extension, known as Disease-Informed Neural Networks (DINNs), has gained attention as a robust framework for parameter estimation. In this work, we apply this DINN technique to a recently proposed hepatitis B virus (HBV) infection dynamics model to predict the transmission of infection within the liver. The model consists of four compartments: uninfected and infected hepatocytes, relaxed circular DNA (rcDNA)-containing capsids, and free viruses. Before estimating the parameters, a structural identifiability analysis is performed to determine the identifiable parameters of this model. Then, we study the impacts of (i) variations in parameter ranges, (ii) experimental noise, (iii) sample size, (iv) network architecture, and (v) learning rate on the performance of DINNs. Furthermore, using experimental data from nine HBV-infected chimpanzees, we observe that DINNs can estimate unknown parameters, capture infection dynamics, and predict disease progression even when experimental data for some model compartments are not available. Additionally, DINNs identify the model parameters that vary significantly across chimpanzees. A global sensitivity analysis is further performed, and the results indicate that significant parameters are consistent with those detected by DINNs. Finally, comparison with nonlinear least-squares fitting and maximum likelihood estimation demonstrates the advantages of DINNs in parameter estimation.