Analysis of a viral infection model with immune impairment and cure rate

Volume 9, Issue 5, pp 3287--3298 http://dx.doi.org/10.22436/jnsa.009.05.115

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Authors

Jianwen Jia - School of Mathematics and Computer Science, Shanxi Normal University, Shanxi, Linfen 041004, P. R. China. Xuewei Shi - School of Mathematics and Computer Science, Shanxi Normal University, Shanxi, Linfen 041004, P. R. China.

Abstract

In this paper, the dynamics behavior of a delayed viral infection model with immune impairment and cure rate is studied. It is shown that there exists three equilibria. By analyzing the characteristic equations, the local stability of the infection-free equilibrium and the immune-exhausted equilibrium of the model are established. In the following, the stability of the positive equilibrium is studied. Furthermore, we investigate the existence of Hopf bifurcation by using a delay as a bifurcation parameter. Finally, numerical simulations are carried out to explain the mathematical conclusions.

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Keywords

• Viral infection
• immune impairment
• cure rate
• Hopf bifurcation
• stability.

MSC

•  34D20
•  92D25.

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