Volume 35, Issue 4
Global and Bifurcation Analysis of an HIV Pathogenesis Model with Saturated Reverse Function

Commun. Math. Res., 35 (2019), pp. 301-317.

Published online: 2019-12

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• Abstract

In this paper, an HIV dynamics model with the proliferation of CD4 T cells is proposed. The authors consider nonnegativity, boundedness, global asymptotic 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 $R_0$ is less than unity. Meanwhile, the model exhibits the phenomenon 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 $R_0$ is greater than unity. It is also proved that the model undergoes Hopf bifurcation from the endemic equilibrium under 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 equilibria and Hopf bifurcation are considered accordingly. In addition, some numerical simulations for justifying the theoretical analysis results are also given in paper.

• Keywords

HIV model, global asymptotical stability, center manifold theory, Hopf bifurcation, backward bifurcation.

34D23, 34D20

liuyongqi1980@163.com (Yongqi Liu)

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@Article{CMR-35-301, author = {Yongqi and Liu and liuyongqi1980@163.com and 6228 and College of Applied Mathematics, Beijing Normal University, Zhuhai, Guangdong, 519087 and Yongqi Liu and Xiaoying and Meng and and 6231 and googleSchool of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, 430073 and Xiaoying Meng}, title = {Global and Bifurcation Analysis of an HIV Pathogenesis Model with Saturated Reverse Function}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {35}, number = {4}, pages = {301--317}, abstract = {

In this paper, an HIV dynamics model with the proliferation of CD4 T cells is proposed. The authors consider nonnegativity, boundedness, global asymptotic 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 $R_0$ is less than unity. Meanwhile, the model exhibits the phenomenon 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 $R_0$ is greater than unity. It is also proved that the model undergoes Hopf bifurcation from the endemic equilibrium under 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 equilibria and Hopf bifurcation are considered accordingly. In addition, some numerical simulations for justifying the theoretical analysis results are also given in paper.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2019.04.02}, url = {http://global-sci.org/intro/article_detail/cmr/13556.html} }
TY - JOUR T1 - Global and Bifurcation Analysis of an HIV Pathogenesis Model with Saturated Reverse Function AU - Liu , Yongqi AU - Meng , Xiaoying JO - Communications in Mathematical Research VL - 4 SP - 301 EP - 317 PY - 2019 DA - 2019/12 SN - 35 DO - http://doi.org/10.13447/j.1674-5647.2019.04.02 UR - https://global-sci.org/intro/article_detail/cmr/13556.html KW - HIV model, global asymptotical stability, center manifold theory, Hopf bifurcation, backward bifurcation. AB -

In this paper, an HIV dynamics model with the proliferation of CD4 T cells is proposed. The authors consider nonnegativity, boundedness, global asymptotic 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 $R_0$ is less than unity. Meanwhile, the model exhibits the phenomenon 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 $R_0$ is greater than unity. It is also proved that the model undergoes Hopf bifurcation from the endemic equilibrium under 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 equilibria and Hopf bifurcation are considered accordingly. In addition, some numerical simulations for justifying the theoretical analysis results are also given in paper.

Yongqi Liu & Xiaoying Meng. (2019). Global and Bifurcation Analysis of an HIV Pathogenesis Model with Saturated Reverse Function. Communications in Mathematical Research . 35 (4). 301-317. doi:10.13447/j.1674-5647.2019.04.02
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