Global and Bifurcation Analysis of an HIV Pathogenesis Model with Saturated Reverse Function

In this paper,an HIV dynamics model with the proliferation of CD4 T cells is proposed.The authors consider nonnegativity,boundedness,global asymp-totic stability of the solutions and bifurcation properties of the steady states.It is proved that the virus is cleared from the host under some condition...

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Veröffentlicht in:数学研究通讯 2019, Vol.35 (4), p.301-317
Hauptverfasser: Liu Yong-qi, Meng Xiao-ying
Format: Artikel
Sprache:eng
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Zusammenfassung:In this paper,an HIV dynamics model with the proliferation of CD4 T cells is proposed.The authors consider nonnegativity,boundedness,global asymp-totic stability of the solutions and bifurcation properties of the steady states.It is proved that the virus is cleared from the host under some conditions if the basic reproduction number R0 is less than unity.Meanwhile,the model exhibits the phe-nomenon of backward bifurcation.We also obtain one equilibrium is semi-stable by using center manifold theory.It is proved that the endemic equilibrium is globally asymptotically stable under some conditions if R0 is greater than unity.It also is proved that the model undergoes Hopf bifurcation from the endemic equilibrium un-der some conditions.It is novelty that the model exhibits two famous bifurcations,backward bifurcation and Hopf bifurcation.The model is extended to incorporate the specific Cytotoxic T Lymphocytes (CTLs) immune response.Stabilities of equi-libria and Hopf bifurcation are considered accordingly.In addition,some numerical simulations for justifying the theoretical analysis results are also given in paper.
ISSN:1674-5647
DOI:10.13447/j.1674-5647.2019.04.02