Abstract
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.
Highlights
People utilize widely mathematical models to investigate viral infections currently, for example, HBV, HCV, HIV, and so on [ – ]
Those results show that the immune delay dominates the intracellular delays in this class of viral infection models, which indicates the human immune system has a special effect in virus infection models with cytotoxic T lymphocytes (CTLs) response, and the human immune system itself is very complicated
People are aware of the complexity of the human immune system in medical science, which coincides with our investigation
Summary
People utilize widely mathematical models to investigate viral infections currently, for example, HBV (hepatitis B virus), HCV (hepatitis C virus), HIV, and so on [ – ]. Γ d d d + βkd d β kd Assuming τ > and ξ = iω (ω > ) is the purely imaginary root of this equation, we obtain iω + d – γ y cos ωτ + iγ y sin ωτ = . Incorporating three delays (a immune delay and two intracellular delays), P is still globally asymptotically stable. By the Routh-Hurwitz criteria, all roots of this equation have negative real parts.
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