A Mathematical Model of Hepatitis B Virus-Liver Cancer Coexistence Dynamics With Immune Response and Treatment

Experimental evidence shows that the immune system plays a crucial role in clearing acute hepatitis B virus (HBV) infection. This study develops a mathematical model to investigate the immune response to HBV and the coexistence of liver cancer within the liver cell population. The model is validated using published patient data from the acute phase of infection. The invasion threshold for disease transmission, represented by the basic reproduction number R0, is derived for populations of uninfected macrophages both in the presence and absence of cancer cells. The basic reproduction number R0 is defined as the number of new HBV and liver cancer cases generated by a single infected macrophage introduced into a fully susceptible population of liver cells. This threshold is then extended to incorporate two treatment controls: nucleotide (nucleoside) analogues (NAs) and interferon-based therapies yielding the control reproduction number Rc. Stability analyses of the virus-free and virus-persistence equilibrium states are performed, and numerical simulations are used to support the analytical results. The influence of different immune components on disease progression is also examined. Simulation results predict the time at which T helper-1 cells exceed cytotoxic T lymphocytes (CTLs), referred to as the time to chronicity, which increases with the proliferation rate of interleukin-10 Ï 3. Further analysis indicates that interleukin-10 promotes HBV persistence by suppressing immune activity, allowing viral evasion and the establishment of chronic infection through inhibition of CTLs responsible for clearing infected cells. To evaluate treatment strategies, antiviral therapies including nucleoside analogues and interferon are incorporated into the model. Results indicate that effective control occurs when Rc