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Abstract
Mathematical models are useful tools to describe the dynamics of infection and predict the role of possible drug combinations. In this paper, we present an analysis of a hepatitis B virus (HBV) model including cytotoxic T lymphocytes (CTL) and antibody responses, under distributed feedback control, expressed as an integral form to predict the effect of a combination treatment with interleukin-2 (IL-2). The method presented in this paper is based on the symmetry properties of Cauchy matrices C(t,s), which allow us to construct and analyze the stability of corresponding integro-differential systems.
Highlights
The hepatitis B virus (HBV) disease is defined as the detection of the HBV surface antigen (HBsAg) on two occasions measured at least six months apart
HBV represents a huge problem for public health, increasing the risk of cirrhosis and hepatocellular carcinoma in the population [1]
This approximation does not allow for realistic predictions, ignoring many crucial factors such as the lifespan of HBV-infected cells that varies greatly due to the strength of the anti-HBV cytotoxic T lymphocytes (CTL) response [20]
Summary
The hepatitis B virus (HBV) disease is defined as the detection of the HBV surface antigen (HBsAg) on two occasions measured at least six months apart. Interferons (α, β, and γ) are cytokines that are endogenously produced by immune system cells in response to viral infections They have antiviral effects, creating a barrier around the cell that reduces the rates of infected cell formation and virus replication [7]. Previous models have tried to predict the effectiveness of antiviral therapy, but without considering the important role of the immune system [17,18,19] This approximation does not allow for realistic predictions, ignoring many crucial factors such as the lifespan of HBV-infected cells that varies greatly due to the strength of the anti-HBV CTL response [20]. The number of CTLs, Z, expands in response to infected cells at a rate cYZ and decays in the absence of infection at a rate bZ The dynamics of both HBV and HCV are similar in their essence. We can adjust the mathematical model of Yousdi et al to our study by adapting the correct course of treatment to each disease
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