Dynamics of spatiotemporal pharmacological models for hepatitis B virus infection under lamivudine and pegylated interferon alfa-2b therapies

Chronic hepatitis B virus (HBV) infection remains a major global health concern due to the limited availability of curative treatment options. In this study, we investigate both analytically and numerically a spatiotemporal mathematical model of HBV infection incorporating pharmacological effects. The model consists of a system of three partial differential equations describing the dynamics and interactions between healthy hepatocytes (S), infected cells (I) and free viral particles (V). The model also considers spatial diffusion and dual-drug treatment of lamivudine and pegylated interferon alfa-2b (PEG-IFN alfa-2b). A general analytical expression is derived to determine the minimal drug dose required to effectively suppress viral replication and eliminate the infection. The basic reproduction number ([Formula: see text]) is calculated as a function of drug effectiveness and model parameters. To illustrate the relevance of the model, we apply it to clinical data from two HBV infected patients undergoing different therapeutic regimens. The first patient received 200 mg daily of lamivudine, while the second was treated with 200 mg of lamivudine daily and 0.2 mg weekly of PEG-IFN alfa-2b. Using nonlinear least squares, we fit the model to clinical data and estimate relevant parameters. In the absence of treatment, we find [Formula: see text]. Pharmacodynamic results show that after 4 weeks, the first patient experienced a [Formula: see text] copies/ml viral decline (64% effectiveness), while the second exhibited a [Formula: see text] copies/ml decline (69% and 64% effectiveness for PEG-IFN alfa-2b and lamivudine, respectively), corresponding to basic reproduction numbers of 185 and 58, respectively. To achieve sustained viral suppression ([Formula: see text]), we optimize the therapies. Lamivudine alone requires 99% effectiveness, which corresponds to a minimum dose of 565.92 mg daily over 350 days. For combination therapy, a PEG-IFN alfa-2b efficacy of 69% and lamivudine efficacy of 94.36% are sufficient to reach [Formula: see text] after 315 days. A Turing instability analysis reveals the emergence of diffusion-driven instabilities and allows the identification of a critical Turing wave number [Formula: see text]. Numerical simulations confirm the analytical predictions and show the formation of circular patterns. These patterns have been identified as having promising diagnostic and therapeutic value. Under treatment, the model predicts a progressive disappearance of infected patterns and a return toward spatial homogeneity. These findings highlight the crucial role of mathematical modeling in refining HBV treatment protocols and provide valuable insights for optimizing antiviral strategies.