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Stability and bifurcation analysis in a viral infection model with delays. (English) Zbl 1422.92167

Summary: In this paper, a class of virus infection models with CTLs response is considered. We incorporate an immune delay and two intracellular delays into the virus infection model. It is found that only incorporating two intracellular delays almost does not change the dynamics of the system, but incorporating an immune delay changes the dynamics of the system very greatly, namely, a Hopf bifurcation and oscillations can appear. Those results show immune delay dominates intracellular delays in some viral infection models, which indicates the human immune system has a special effect in virus infection models with CTLs response, and the human immune system itself is very complicated. In fact, people are aware of the complexity of the human immune system in medical science, which coincides with our investigating. We also investigate the global Hopf bifurcation of the system with the immune delay as a bifurcation parameter.

MSC:

92D30 Epidemiology
34K20 Stability theory of functional-differential equations
92C50 Medical applications (general)
92C60 Medical epidemiology
34K60 Qualitative investigation and simulation of models involving functional-differential equations
37N25 Dynamical systems in biology
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