Modelling and Simulation of the Spread of HBV Disease with Infectious Latent

Abstract

This paper studies the global behavior of the spread of HBV using a SEIR model with a constant vaccination rate. The infectivity during the incubation period is considered as a second way of transmission. The basic reproduction number R 0 is derived as a function of the two contact rates β1 and β2 . There is a disease free equilibrium point (DFE) of our model. When R 0 < 1, the (DFE) is asymptotically stable. On the other hand, if R 0 > 1, there is a unique endemic equilibrium. We proved that the endemic equilibrium was globally asymptotically stable when R 0 > 1 and that the disease persisted in the population. These results are original for our model with vaccination and two contact rates.