Mathematical Model for the Acute Hepatitis C Virus Infection Subject to Immune System Response and Therapy

Seleman Ismail, Livingstone Luboobi, Yaw Nkansah-Gyekye

Abstract


Hepatitis C virus (HCV) is a source of chronic hepatitis C infection that can destroy the liver when proper therapeutic intervention is not executed early. For the purpose of studying the dynamics of the disease during acute infection, a deterministic mathematical model incorporating the effect of immune system and therapy has been formulated. The model is a system of non-linear ordinary differential equations. The disease-free equilibrium point  during therapy has been computed. Furthermore, the basic reproductive number and effective reproductive number have been computed using the next generation method. The sensitivity indices of  relating to each parameter in the model were computed. It is found that is most sensitive to the drug inhibiting efficacy of viral replication parameter. Thus, it implies that an increase in the value of  will reduce the rate of viral replication leading to the decrease or eradication of the HCV morbidity. By using the estimated parametric values, we found that, which attests that therapeutic strategy is absolutely effective in reducing intensity of the disease and hence preventing evolution to chronic state.


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