Co-dynamics of hepatitis B and C viruses under the influence of CTL immunity

Understanding the cytotoxic T lymphocyte (CTL) immune response against hepatitis B virus (HBV) and hepatitis C virus (HCV) infections is crucial, as these infections can lead to liver cirrhosis and cancer. Mathematical models provide valuable support for biological and medical research by helping to understand the within-host dynamics of single or multiple viral infections and by aiding the development of effective drug therapies. This study aims to develop an HBV and HCV co-infection model to investigate the role of CTL immunity in combating both viruses. The model incorporates latently and actively infected hepatocytes, multiple distributed-time delays, and a saturated incidence function. To confirm the model’s well-posedness, we demonstrate that its solution remains non-negative and ultimately bounded. The model’s long-term behavior is analyzed by identifying nine equilibrium points and deriving conditions for their existence and stability. These conditions are determined based on key threshold parameters that govern system dynamics. The global stability of all equilibria is proven using Lyapunov’s method combined with LaSalle’s invariance principle. The theoretical findings are further supported and validated through numerical simulations. A sensitivity analysis is conducted to identify the parameter with the greatest influence on model behavior. Additionally, we examine the effects of antiviral therapy, time delays, and CTL immunity. The results indicate that both the length of the delay period and the efficacy of antiviral drugs independently contribute to reducing HBV and HCV levels, thereby improving liver health. Moreover, enhancing the activation rates of CTL immunity increases the population of uninfected hepatocytes and further suppresses viral replication during co-infection. This suggests that certain treatments could be developed to extend the delay period. Additionally, the study underscores the significance of immunotherapy in enhancing the immune system’s response. By stimulating the immune system to function more effectively, immunotherapy can play a vital role in combating viral infections. Effective treatment of infected individuals is crucial in limiting the spread of infectious diseases.