A Mathematical Model for the Acute Hepatitis C Virus Dynamics: Liver Regeneration and Activity of Immune System

Seleman Ismail, Livingstone Luboobi

Abstract


Acute hepatitis C infection (AHCI) being an initial stage of hepatitis C virus(HCV) infection can lead to chronic hepatitis infection, and ultimately to cirrhotic hepatitis, in the absence of early strategic intervention. Moreover, the immune system activity and liver regeneration through hepatocytes proliferation have not fully assisted to obstruct potential disease progression to cirrhotic hepatitis although some infected people can clear the virus spontaneously in AHCI. Thus, this paper introduces a deterministic mathematical model formulated to investigate the effect of immune system on the transmission dynamics of HCV with hepatocytes proliferation and spontaneous recovery of infected hepatocytes. The model is a system of non-linear ordinary differential equations, from which we determined the disease free equilibrium point,  and then derived the basic reproductive number,  using the next generation matrix operator. Sensitivity indices of  relating to some parameters of the model were computed, whereby the parameters for the maximum hepatocytes proliferation rate, a  and virus production rate,  are altogether

most positively sensitive whereas the parameter for the spontaneous recovery rate of infected hepatocytes,  S  is the most negatively sensitive one. Numerical analysis of the model has been done to illustrate certain analytical results of the model. Thus, we recommend that appropriate preventive measures should be taken early after infection onset for a patient who is incapable of clearing the virus spontaneously to reduce the intensity of HCV infection and hence stop possible disease progression to more fatal stages of infection.


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