CENTER MANIFOLD ANALYSIS AND HOPF BIFURCATION OF WITHIN-HOST VIRUS MODEL

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MOHEBBI HOSSEIN; AMINATAEI AZIM; POURBASHASH HOSSEIN; ATAEI PIRKOOH ANJILA

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Journal Paper

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Journal: Computational Methods for Differential Equations Year:2018 | Volume:6 | Issue:3 Page(s): 266-279

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Title

CENTER MANIFOLD ANALYSIS AND HOPF BIFURCATION OF WITHIN-HOST VIRUS MODEL

Author(s)

MOHEBBI HOSSEIN | AMINATAEI AZIM | POURBASHASH HOSSEIN | ATAEI PIRKOOH ANJILA | Issue Writer Certificate

Keywords

WITHIN-HOST VIRUS MODEL

LOCAL AND GLOBAL STABILITY

CENTER MANIFOLD

REPRODUCTION NUMBER

HOPF BIFURCATION

Abstract

A mathematical model of a within-host viral infection is presented. A local stability analysis of the model is conducted in two ways. At first, the basic REPRODUCTION NUMBER of the system is calculated. It is shown that when the REPRODUCTION NUMBER falls below unity, the disease free equilibrium (DFE) is globally asymptotically stable, and when it exceeds unity, the DFE is unstable and there exists a unique infectious equilibrium which may or may not be stable. In the case of instability, there exists an asymptotically stable periodic solution. Secondly, an analysis of local CENTER MANIFOLD shows that whenR0=1, a transcritical bifurcation occurs where upon increasing R0 greater than one the DFE loses stability and a locally asymptotically positive infection equilibrium appears.

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APA: Copy

MOHEBBI, HOSSEIN, AMINATAEI, AZIM, POURBASHASH, HOSSEIN, & ATAEI PIRKOOH, ANJILA. (2018). CENTER MANIFOLD ANALYSIS AND HOPF BIFURCATION OF WITHIN-HOST VIRUS MODEL. COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, 6(3), 266-279. SID. https://sid.ir/paper/345664/en

Vancouver: Copy

MOHEBBI HOSSEIN, AMINATAEI AZIM, POURBASHASH HOSSEIN, ATAEI PIRKOOH ANJILA. CENTER MANIFOLD ANALYSIS AND HOPF BIFURCATION OF WITHIN-HOST VIRUS MODEL. COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS[Internet]. 2018;6(3):266-279. Available from: https://sid.ir/paper/345664/en

IEEE: Copy

HOSSEIN MOHEBBI, AZIM AMINATAEI, HOSSEIN POURBASHASH, and ANJILA ATAEI PIRKOOH, “CENTER MANIFOLD ANALYSIS AND HOPF BIFURCATION OF WITHIN-HOST VIRUS MODEL,” COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, vol. 6, no. 3, pp. 266–279, 2018, [Online]. Available: https://sid.ir/paper/345664/en

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