## Hopf bifurcation and stability of periodic solutions for delay differential model of HIV infection of CD4 T-cells.(English)Zbl 1474.92060

Summary: This paper deals with stability and Hopf bifurcation analyses of a mathematical model of HIV infection of $$\text{CD} 4^+$$ T-cells. The model is based on a system of delay differential equations with logistic growth term and antiretroviral treatment with a discrete time delay, which plays a main role in changing the stability of each steady state. By fixing the time delay as a bifurcation parameter, we get a limit cycle bifurcation about the infected steady state. We study the effect of the time delay on the stability of the endemically infected equilibrium. We derive explicit formulae to determine the stability and direction of the limit cycles by using center manifold theory and normal form method. Numerical simulations are presented to illustrate the results.

### MSC:

 92C60 Medical epidemiology 92D30 Epidemiology 34K20 Stability theory of functional-differential equations 37N25 Dynamical systems in biology

dde23
Full Text:

### References:

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