Dynamical Analysis of a Delayed HIV Virus Dynamic Model with Cell-to-Cell Transmission and Apoptosis of Bystander Cells
In this paper, a delayed viral dynamical model that considers two different transmission methods of the virus and apoptosis of bystander cells is proposed and investigated. The basic reproductive number R0 of the model is derived. Based on the basic reproductive number, we prove that the disease-fre...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/2313102 |
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| _version_ | 1850105062798393344 |
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| author | Tongqian Zhang Junling Wang Yi Song Zhichao Jiang |
| author_facet | Tongqian Zhang Junling Wang Yi Song Zhichao Jiang |
| author_sort | Tongqian Zhang |
| collection | DOAJ |
| description | In this paper, a delayed viral dynamical model that considers two different transmission methods of the virus and apoptosis of bystander cells is proposed and investigated. The basic reproductive number R0 of the model is derived. Based on the basic reproductive number, we prove that the disease-free equilibrium E0 is globally asymptotically stable for R0<1 by constructing suitable Lyapunov functional. For R0>1, by regarding the time delay as bifurcation parameter, the existence of local Hopf bifurcation is investigated. The results show that time delay can change the stability of endemic equilibrium and cause periodic oscillations. Finally, we give some numerical simulations to illustrate the theoretical findings. |
| format | Article |
| id | doaj-art-404f8db69ff8446991e1cac4d1e13102 |
| institution | DOAJ |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-404f8db69ff8446991e1cac4d1e131022025-08-20T02:39:12ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/23131022313102Dynamical Analysis of a Delayed HIV Virus Dynamic Model with Cell-to-Cell Transmission and Apoptosis of Bystander CellsTongqian Zhang0Junling Wang1Yi Song2Zhichao Jiang3College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaSchool of Liberal Arts and Sciences, North China Institute of Aerospace Engineering, Langfang 065000, ChinaIn this paper, a delayed viral dynamical model that considers two different transmission methods of the virus and apoptosis of bystander cells is proposed and investigated. The basic reproductive number R0 of the model is derived. Based on the basic reproductive number, we prove that the disease-free equilibrium E0 is globally asymptotically stable for R0<1 by constructing suitable Lyapunov functional. For R0>1, by regarding the time delay as bifurcation parameter, the existence of local Hopf bifurcation is investigated. The results show that time delay can change the stability of endemic equilibrium and cause periodic oscillations. Finally, we give some numerical simulations to illustrate the theoretical findings.http://dx.doi.org/10.1155/2020/2313102 |
| spellingShingle | Tongqian Zhang Junling Wang Yi Song Zhichao Jiang Dynamical Analysis of a Delayed HIV Virus Dynamic Model with Cell-to-Cell Transmission and Apoptosis of Bystander Cells Complexity |
| title | Dynamical Analysis of a Delayed HIV Virus Dynamic Model with Cell-to-Cell Transmission and Apoptosis of Bystander Cells |
| title_full | Dynamical Analysis of a Delayed HIV Virus Dynamic Model with Cell-to-Cell Transmission and Apoptosis of Bystander Cells |
| title_fullStr | Dynamical Analysis of a Delayed HIV Virus Dynamic Model with Cell-to-Cell Transmission and Apoptosis of Bystander Cells |
| title_full_unstemmed | Dynamical Analysis of a Delayed HIV Virus Dynamic Model with Cell-to-Cell Transmission and Apoptosis of Bystander Cells |
| title_short | Dynamical Analysis of a Delayed HIV Virus Dynamic Model with Cell-to-Cell Transmission and Apoptosis of Bystander Cells |
| title_sort | dynamical analysis of a delayed hiv virus dynamic model with cell to cell transmission and apoptosis of bystander cells |
| url | http://dx.doi.org/10.1155/2020/2313102 |
| work_keys_str_mv | AT tongqianzhang dynamicalanalysisofadelayedhivvirusdynamicmodelwithcelltocelltransmissionandapoptosisofbystandercells AT junlingwang dynamicalanalysisofadelayedhivvirusdynamicmodelwithcelltocelltransmissionandapoptosisofbystandercells AT yisong dynamicalanalysisofadelayedhivvirusdynamicmodelwithcelltocelltransmissionandapoptosisofbystandercells AT zhichaojiang dynamicalanalysisofadelayedhivvirusdynamicmodelwithcelltocelltransmissionandapoptosisofbystandercells |