Experimental evidence confirms that interleukin-10 plays a critical role in clearing acute hepatitis B virus infection. This paper aims to develops a mathematical model to explore the dynamics of how the immune system responds to hepatitis B virus (HBV) and coexisting liver cancer within the liver cell population. Unlike previous models; we categorize liver cells into various stages of infection. We determine the invasion probability for transmission dynamics, specifically the basic reproduction number, ℝ0, for populations of uninfected macrophages with and without cancer cells. Stability analyses of virus-free and virus equilibrium states are provided, along with numerical simulations to validate analytical findings. The impact of different branches of the immune response on model dynamics is assessed. Simulations predict the time at which T helper-1 cells surpass cytotoxic T cells (switching time), correlating positively with the proliferation rate of interleukin-10 (ρ3). Further numerical simulations demonstrate that interleukin-10 contributes to HBV persistence by inhibiting the immune response, thereby allowing the virus to evade immune surveillance and establish chronic infection through the suppression of cytotoxic T lymphocytes (CTLs), which are essential for clearing infected cells.

The authors have declared no competing interest.

This study did not receive any funding

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