Analysis and simulation of a stochastic reaction–diffusion model for HBV infection under antiviral treatment

Hepatitis B virus infection remains a major global health concern. It is characterized by complex intra-host interactions and strong spatiotemporal variability. Classical deterministic models often assume a constant intracellular delay, overlooking the random nature of viral replication timing and treatment response. To address this limitation, we develop a stochastic delay framework that accounts for biological variability and spatial diffusion, allowing a more realistic understanding of Hepatitis B virus infection dynamics under antiviral therapy. We propose a reaction-diffusion model with a stochastic intracellular delay and antiviral treatment. The model describes the interactions between healthy hepatocytes, infected cells and free viral particles within a two-dimensional spatial domain. Numerical simulations were performed to investigate the effects of stochastic time delay and treatment efficacy on infection patterns. A global sensitivity analysis using partial rank correlation coefficients was also conducted to identify key parameters influencing the steady-state viral load. The sensitivity analysis indicates that viral production and infectivity are the main drivers of infection persistence, while viral clearance and treatment efficacy strongly reduce viral load. A stochastic delay induces oscillations in infection dynamics. This reflects variability in the time required for newly infected cells to become infectious. Increasing the delay enhances fluctuations in the infected cell population but leave the mean viral concentration relatively stable under effective therapy. Spatially, the model reproduces heterogeneous infection patterns whose amplitudes decrease under stronger treatment, illustrating how therapy promotes spatial homogenization and viral suppression. The stochastic reaction-diffusion model provides a comprehensive framework for exploring the combined effects of randomness, spatial diffusion and antiviral treatment in hepatitis B virus dynamics. It extends existing deterministic approaches by capturing the stochastic variability inherent to viral replication and therapy response. These findings highlight the importance of integrating stochastic and spatial processes in hepatitis B virus modeling and suggest that combined inhibition of viral production and infectivity with enhanced clearance can represent an optimal therapeutic strategy.