Effect of vaccination and treatment on the MSEICR model of the transmission of hepatitis B virus

Abstract

Abstract This article studies a development of SEIR standard model for the spread of hepatitis B virus. The model is developed by considering immunized and carrier compartments of population. The model includes immunized, suspected, exposed, infected, carrier, and recovered compartments and written as MSEICR. Some of new born and the suspected are given vaccines and the infected is given a treatment. These strategies aim to reduce transmissions of hepatitis B virus in the population. The existence and stability of endemic and non-endemic equilibrium points are analysed via basic reproduction number (ℛ 0 ) which is derived from the next generation matrix method. The results showed that the endemic equilibrium point does not exist when ℛ 0 < 1. The endemic will appear when the value of ℛ 0 > 1. Sensitivity analyses showed that vaccination and treatment may reduce the spread of hepatitis B virus and also eliminate endemic condition. Some simulations were conducted to visualize the effects of vaccination and treatment on the existence and stability of endemic equilibrium point.

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