Abstract
We formulate and systematically study the global dynamics of a simple model of hepatitis B virus in terms of delay differential equations. This model has two important and novel features compared to the well-known basic virus model in the literature. Specifically, it makes use of the more realistic standard incidence function and explicitly incorporates a time delay in virus production. As a result, the infection reproduction number is no longer dependent on the patient liver size (number of initial healthy liver cells). For this model, the existence and the component values of the endemic steady state are explicitly dependent on the time delay. In certain biologically interesting limiting scenarios, a globally attractive endemic equilibrium can exist regardless of the time delay length.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 140-153 |
| Number of pages | 14 |
| Journal | Journal of Biological Dynamics |
| Volume | 2 |
| Issue number | 2 |
| DOIs | |
| State | Published - Apr 2008 |
Fingerprint
ASJC Scopus subject areas
- Ecology, Evolution, Behavior and Systematics
- Ecology
Cite this
Dynamics of a delay differential equation model of hepatitis B virus infection. / Gourley, Stephen A.; Kuang, Yang; Nagy, John D.
In: Journal of Biological Dynamics, Vol. 2, No. 2, 04.2008, p. 140-153.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Dynamics of a delay differential equation model of hepatitis B virus infection.
AU - Gourley, Stephen A.
AU - Kuang, Yang
AU - Nagy, John D.
PY - 2008/4
Y1 - 2008/4
N2 - We formulate and systematically study the global dynamics of a simple model of hepatitis B virus in terms of delay differential equations. This model has two important and novel features compared to the well-known basic virus model in the literature. Specifically, it makes use of the more realistic standard incidence function and explicitly incorporates a time delay in virus production. As a result, the infection reproduction number is no longer dependent on the patient liver size (number of initial healthy liver cells). For this model, the existence and the component values of the endemic steady state are explicitly dependent on the time delay. In certain biologically interesting limiting scenarios, a globally attractive endemic equilibrium can exist regardless of the time delay length.
AB - We formulate and systematically study the global dynamics of a simple model of hepatitis B virus in terms of delay differential equations. This model has two important and novel features compared to the well-known basic virus model in the literature. Specifically, it makes use of the more realistic standard incidence function and explicitly incorporates a time delay in virus production. As a result, the infection reproduction number is no longer dependent on the patient liver size (number of initial healthy liver cells). For this model, the existence and the component values of the endemic steady state are explicitly dependent on the time delay. In certain biologically interesting limiting scenarios, a globally attractive endemic equilibrium can exist regardless of the time delay length.
UR - http://www.scopus.com/inward/record.url?scp=58049164600&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=58049164600&partnerID=8YFLogxK
U2 - 10.1080/17513750701769873
DO - 10.1080/17513750701769873
M3 - Article
VL - 2
SP - 140
EP - 153
JO - Journal of Biological Dynamics
JF - Journal of Biological Dynamics
SN - 1751-3758
IS - 2
ER -