FAN, Xinyue; BRAUNER, Claude-Michel; WITTKOP, Linda

doi:10.3934/dcdsb.2012.17.2359

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FAN, Xinyue
School of Mathematical Sciences

BRAUNER, Claude-Michel
School of Mathematical Sciences
Institut de Mathématiques de Bordeaux [IMB]

WITTKOP, Linda
Epidémiologie et Biostatistique [Bordeaux]

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Discrete and Continuous Dynamical Systems - Series B. 2012-10, vol. 17, n° 7, p. 27

American Institute of Mathematical Sciences

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We consider a model of disease dynamics in the modeling of Human Immunodeficiency Virus (HIV). The system consists of three ODEs for the concentrations of the target T cells, the infected cells and the virus particles. There are two main parameters, $N$, the total number of virions produced by one infected cell, and $r$, the logistic parameter which controls the growth rate. The equilibria corresponding to the infected state are asymptotically stable in a region $(\mathcal I)$, but unstable in a region $(\mathcal P)$. In the unstable region, the levels of the various cell types and virus particles oscillate, rather than converging to steady values. Hopf bifurcations occurring at the interfaces are fully investigated via several techniques including asymptotic analysis. The Hopf points are connected through a ''snake" of periodic orbits. Numerical results are presented.< Réduire

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HIV modeling

stability

Hopf bifurcation

orbits

snakes

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Mathematical analysis of a HIV model with quadratic logistic growth term

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