A fractional order model of hepatitis B transmission under the effect of vaccination

Abstract

In this paper we present a fractional order mathematical model to explain the spread of Hepatitis B Virus (HBV) in a non-constant population. The model we propose includes both vertical and horizontal transmission of the infection and also vaccination at birth and vaccination of the susceptible class. We also use a frequency dependent transmission rate in the model. We give results on existence of equilibrium points of the model and analyze the stability of the disease-free equilibrium. Finally, numerical simulations of the model are presented.