Dynamical Analysis of Transmission of Hepatitis B and C Viruses with External Source of disease by Mathematical Model

Abstract

In this paper, we develop a deterministic mathematical model of the Hepatitis B and C viruses transmission in population, which allows transmission by two way vertical such as from pregnant mother to fetus and horizontal. Also, by two way through direct contact and due to the external source of infective such as blood transfusion or other. In reality, we know that there is a vaccination against the hepatitis B virus but so far, there is no vaccine against the hepatitis C virus this is why it is considered more dangerous than hepatitis B. Furthermore, we study the vaccination effect with the failure in the vaccine. We propose an SVIBICR model using a system of ordinary differential equations. First the major basic analysis, like the uniqueness, boundedness and positivity of the solution for the proposed model. Second the existence of all biological equilibrium points, basic reproduction number and stability analysis of all equilibrium points. The numerical simulation indicated to confirm the analytic results and the government must apply all control strategies in combating hepatitis virus at short periods of time.