Multiple Endemic Solutions in an Epidemic Hepatitis B Model without Vertical Transmission

Abstract

This paper examines the dynamics of Hepatitis B via a Susceptible Exposed Infectious Recovered (SEIR) type epidemic model. Previous studies have shown that Hepatitis B is characterized by multiple endemic solutions, a matter which may be of concern in developing control strategies. We identify the possible causes of multiple endemic solutions in a Hepatitis B model and conclude that the dependance of the probability of carriage development ( q (Λ)) on the force of infection (Λ) is the main reason for multiple endemicity. Other factors such as a large proportion of infants that are not vaccinated ( ω ) may also enhance the possibility of multiple endemicity. The role of carriers may also play a key role in the possibility of such complex dynamics, i.e. , when infectiousness of carriers-( α ) is high, the probability of existence of multiple endemic equilibrium solutions is increased. In our arguments, the traditional reproduction number R 0 < 1 which we define here by a function G (0) < 1 does not imply stability of disease-free equilibrium.