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

I. A. Moneim^1,2, H. A. Khalil^1,3

¹Department of Basic and Applied Science, Unaizah Community College, Qassim University, Unaizah, Saudi Arabia.
²Department of Scientific Computing, Faculty of Computers and Information, Benha University, Benha, Egypt.
³Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt.

DOI: 10.4236/am.2015.65070                

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 R0 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 R0 < 1, the (DFE) is asymptotically stable. On the other hand, if R0 > 1, there is a unique endemic equilibrium. We proved that the endemic equilibrium was globally asymptotically stable when R0 > 1 and that the disease persisted in the population. These results are original for our model with vaccination and two contact rates.

Keywords

HBV Modelling, Global Stability, Simulation, Two Contact Rates, Basic Reproduction Number R0

Conflicts of Interest

The authors declare no conflicts of interest.

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