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Dynamics of a HIV-1 infection model with cell-mediated immune response and intracellular delay. (English) Zbl 1169.92033
Summary: We consider a mathematical model for HIV-1 infection with intracellular delay and cell-mediated immune response. A novel feature is that both cytotoxic T lymphocytes (CTLs) and the intracellular delay are incorporated into the model. We obtain a necessary and sufficient condition for the global stability of the infection-free equilibrium and give sufficient conditions for the local stability of the two infection equilibria: one without CTLs being activated and the other with.
We also perform some numerical simulations which support the obtained theoretical results. These results show that larger intracellular delay may help eradicate the virus, while the activation of CTLs can only help reduce the virus load and increase the healthy CD$$_4^+$$ cells population in the long term sense.

##### MSC:
 92C50 Medical applications (general) 92C60 Medical epidemiology 34K20 Stability theory of functional-differential equations 34K60 Qualitative investigation and simulation of models involving functional-differential equations 65C20 Probabilistic models, generic numerical methods in probability and statistics
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