Stability ‎a‎nalysis of the transmission dynamics of an HBV model

Subject Areas : International Journal of Industrial Mathematics

R. Akbari ¹ , A. Vahidian Kamyad ² , A. A. Heydari ³ , A. Heydari ⁴

1 - Department of Mathematical Sciences, Payame Noor University ,P.O.Box 19395-3697 , Tehran ,Iran.
2 - Department of Mathematics Sciences , University of Ferdowsi, Mashhad, Iran.
3 - Research Center for Infection Control and Hand Hygiene, Mashhad University Of Medical Sciences, Mashhad, Iran.
4 - Department of Mathematical Sciences, Payame Noor University, P. O. Box 19395-3697, Tehran, Iran.

Received: 2016-02-14 Accepted : 2016-02-14 Published : 2016-04-01

Keywords: Hepatitis B virus (HBV), Basic reproduction number ($R_, ‎G‎ompound matrices, Global ‎stability.‎,

Abstract :

‎Hepatitis B virus (HBV) infection is a major public health problem in the world today‎. ‎A mathematical model is formulated to describe the spread of hepatitis B‎, ‎which can be controlled by vaccination as well as treatment‎. ‎We study the dynamical behavior of the system with fixed control for both vaccination and treatment‎. ‎The results shows that the dynamics of the model is completely determined by the basic reproductive number R_0. ‎if R_0<1, ‎the disease-free equilibrium is globally asymptotically stable by using approach that given by Kamgang and Sallet‎. ‎Then the authors prove that if R_0>1, ‎the disease-free equilibrium is unstable and the disease is uniformly persistent‎. ‎Furthermore‎, ‎If R_0>1, ‎the unique endemic equilibrium is globally asymptotically stable by using a generalization of the Poincar e-Bendixson ‎criterion.‎