Vertical Transmission of Hepatitis-C Virus (HCV) with Optimal Control on Treatment Expenses

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Nita H. Shah
Bijal M. Yeolekar
Nehal J. Shukla


The hepatitis C virus infects the liver which does not display an early symptom. As such an infected individual recognize these infections only at the later stage. Around the globe, many individuals suffer from HCV. In this study, we developed a transmission of HCV with five components viz. susceptible, acute infected, chronically infected, hospitalized and recovered individuals. The basic reproduction number was calculated using next-generation matrix. The stability of the model was found at equilibrium points. The disease-free equilibrium is locally asymptotically stable if R0 < 1 otherwise unstable. The control in terms of the treatment cost by government and expenses incurred by patients has been optimized. The model was supported by strong numerical data. It is observed to optimize the maximum amount for treatment cost paid by the Government and minimum amount of treatment paid by the infected individuals; it will help us in decreasing the burden of Hepatitis C in the population. Furthermore, critical factors in terms of model parameters were reported and discussed.

Hepatitis C virus, acute infection, chronic infection, stability, treatment cost, optimal control.

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How to Cite
Shah, N. H., Yeolekar, B. M., & Shukla, N. J. (2018). Vertical Transmission of Hepatitis-C Virus (HCV) with Optimal Control on Treatment Expenses. Asian Research Journal of Mathematics, 8(4), 1-12.
Original Research Article