Hepatitis B virus (HBV) infection is a deadly liver disease. The main aim of this work is to explore the role of cytoplasmic recycling of rcDNA-containing capsids in the hepatitis B virus (HBV) infection. To this purpose, considering the recycling of capsids, a noval mathematical model is proposed in order to understand the dynamics of this viral infection in a better way. Through a rigorous comparison with the experimental data obtained from two chimpanzees, the proposed model exhibits a robust alignment with the dynamics of infection. The effects of three parameters (recycling rate, virus production rate, and volume fraction of newly produced capsids) are examined, revealing an interesting observation: the inclusion of recycling reverses the influence of both virus production rate and the volume fraction of newly produced capsids in infection. A comprehensive global sensitivity analysis is conducted to identify the most positively as well as negatively sensitive parameters for each model compartment. In conclusion, this study underscores that the accumulation of rcDNA-containing capsids within the infected hepatocyte is a key factor contributing to the exacerbation of the disease. In addition, another major finding of our study is that due to recycling of capsids, the number of released viruses increases in spite of low virus production rate. In other words, the recycling of capsids acts as a positive feedback loop in the viral infection. 

Hepatitis B virus (HBV) infection is a major public health concern throughout the world. It can be treated effectively through proper medication and vaccination, although it is very difficult to cure, especially in people who have had the chronic infection. So, it is necessary to pay proper attention for its eradication. In this study, two nonlinear fractional-order HBV infection models with recycling effects of capsids are presented via the Caputo derivative. Each model contains four compartments, namely, susceptible hepatocytes, infected hepatocytes, HBV capsids, and viruses. In the first model, the order of fractional derivatives is equal for each compartment, whereas, in the second model, the order is incommensurate. The existence and uniqueness of solutions for both models are discussed separately. The parameters are estimated in order to vali date the proposed model with experimental data obtained from a chimpanzee. Stability analyses are carried out for both models theoretically. The models are solved numerically using the predictor–corrector Adams–Bashforthm–Moulton method (for commensurate order) and implicit product integration of trape zoidal type method (for incommensurate order) with various choices of frac tional orders and initial conditions. All the results are presented graphically. Interestingly, the results reveal the importance of fractional-order derivatives in capturing the dynamics of HBV transmission in the host. It is also noticed that with the decrease in the order of fractional derivative, the peak level of infection decreases, but the disease takes a long time to be cured. 

In this paper, we investigate the dynamics of hepatitis B virus infection taking into account the implementation of combination therapy through mathe matical modeling. This model is established considering the interplay between uninfected cells, infected cells, capsids, and viruses. Three drugs are considered for specific roles: (i) pegylated interferon (PEG-IFN) for immune modulation, (ii) lamivudine (LMV) as a reverse-transcriptase inhibitor, and (iii) entecavir (ETV) to block capsid recycling. Using these drugs, three combination therapies are introduced, specifically CT: PEG-IFN+LMV, CT: PEG-IFN+ETV, and CT: PEG IFN+LMV+ETV. As a result, when LMV is used in combination therapy with PEG-IFN and ETV, the impacts of ETV become insignificant. In conclusion, if the appropriate drug effectively inhibits reverse-transcription, there’s no need for an additional inhibitor to block capsid recycling.