STABILITY AND BIFURCATION ANALYSIS OF A VIRAL INFECTION MODEL WITH DELAYED IMMUNE RESPONSE

Hui Chen; Rui Xu

doi:10.11948/2017033

2017 Volume 7 Issue 2

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Hui Chen, Rui Xu. STABILITY AND BIFURCATION ANALYSIS OF A VIRAL INFECTION MODEL WITH DELAYED IMMUNE RESPONSE[J]. Journal of Applied Analysis & Computation, 2017, 7(2): 532-553. doi: 10.11948/2017033

Citation:

Hui Chen, Rui Xu. STABILITY AND BIFURCATION ANALYSIS OF A VIRAL INFECTION MODEL WITH DELAYED IMMUNE RESPONSE[J]. Journal of Applied Analysis & Computation, 2017, 7(2): 532-553. doi: 10.11948/2017033

STABILITY AND BIFURCATION ANALYSIS OF A VIRAL INFECTION MODEL WITH DELAYED IMMUNE RESPONSE

Hui Chen^1,2,
Rui Xu¹

1 Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, No.97 Heping West Road, Shijiazhuang 050003, Hebei Province, China;
2 Department of Epidemiology, School of Public Heath, The Fourth Military Medical University, No.169, Changle West Road, Xian, Shanxi, 710032, China

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Abstract

Abstract

In this paper, we study a viral infection model with an immunity time delay accounting for the time between the immune system touching antigenic stimulation and generating CTLs. By calculation, we derive two thresholds to determine the global dynamics of the model, i.e., the reproduction number for viral infection R₀ and for CTL immune response R₁. By analyzing the characteristic equation, the local stability of each feasible equilibrium is discussed. Furthermore, the existence of Hopf bifurcation at the CTL-activated infection equilibrium is also studied. By constructing suitable Lyapunov functionals, we prove that when R₀ ≤ 1, the infection-free equilibrium is globally asymptotically stable,when R₀>1 and R₁ ≤ 1, the CTLinactivated infection equilibrium is globally asymptotically stable,Numerical simulation is carried out to illustrate the main results in the end.
- Immunity time delay /
- thresholds /
- CTL immune response /
- Hopf bifurcation /
- global stability

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References

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