Numerical Analysis for a Fractional Differential Time-Delay Model of HIV Infection of CD4+ T-Cell Proliferation under Antiretroviral Therapy
We study a fractional differential model of HIV infection of CD4+ T-cell, in which the CD4+ T-cell proliferation plays an important role in HIV infection under antiretroviral therapy. An appropriate method is given to ensure that both the equilibria are asymptotically stable for τ≥0. We calculate th...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/291614 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832563531858313216 |
|---|---|
| author | Yiliang Liu Peifen Lu Ivan Szanto |
| author_facet | Yiliang Liu Peifen Lu Ivan Szanto |
| author_sort | Yiliang Liu |
| collection | DOAJ |
| description | We study a fractional differential model of HIV infection of CD4+ T-cell, in which the CD4+ T-cell proliferation plays an important role in HIV infection under antiretroviral therapy. An appropriate method is given to ensure that both the equilibria are asymptotically stable for τ≥0. We calculate the basic reproduction
number R0, the IFE E0, two IPEs E1* and E2*, and so on, and judge the stability of the equilibrium. In addition, we describe the dynamic behaviors of the fractional HIV model by using the Adams-type predictor-corrector method algorithm. At last, we extend the model to incorporate the term which we consider the loss of virion and a bilinear term during attacking the target cells. |
| format | Article |
| id | doaj-art-ed0e8ee954754c96a16bb71e296ec59d |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ed0e8ee954754c96a16bb71e296ec59d2025-02-03T01:20:04ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/291614291614Numerical Analysis for a Fractional Differential Time-Delay Model of HIV Infection of CD4+ T-Cell Proliferation under Antiretroviral TherapyYiliang Liu0Peifen Lu1Ivan Szanto2College of Sciences, Guangxi University for Nationalities, Nanning, Guangxi 530006, ChinaCollege of Sciences, Guangxi University for Nationalities, Nanning, Guangxi 530006, ChinaDepartamento de Matematica, Universidad Tecnica Federico Santa Maria, Casilla 110-V, Valparaiso, ChileWe study a fractional differential model of HIV infection of CD4+ T-cell, in which the CD4+ T-cell proliferation plays an important role in HIV infection under antiretroviral therapy. An appropriate method is given to ensure that both the equilibria are asymptotically stable for τ≥0. We calculate the basic reproduction number R0, the IFE E0, two IPEs E1* and E2*, and so on, and judge the stability of the equilibrium. In addition, we describe the dynamic behaviors of the fractional HIV model by using the Adams-type predictor-corrector method algorithm. At last, we extend the model to incorporate the term which we consider the loss of virion and a bilinear term during attacking the target cells.http://dx.doi.org/10.1155/2014/291614 |
| spellingShingle | Yiliang Liu Peifen Lu Ivan Szanto Numerical Analysis for a Fractional Differential Time-Delay Model of HIV Infection of CD4+ T-Cell Proliferation under Antiretroviral Therapy Abstract and Applied Analysis |
| title | Numerical Analysis for a Fractional Differential Time-Delay Model of HIV Infection of CD4+ T-Cell Proliferation under Antiretroviral Therapy |
| title_full | Numerical Analysis for a Fractional Differential Time-Delay Model of HIV Infection of CD4+ T-Cell Proliferation under Antiretroviral Therapy |
| title_fullStr | Numerical Analysis for a Fractional Differential Time-Delay Model of HIV Infection of CD4+ T-Cell Proliferation under Antiretroviral Therapy |
| title_full_unstemmed | Numerical Analysis for a Fractional Differential Time-Delay Model of HIV Infection of CD4+ T-Cell Proliferation under Antiretroviral Therapy |
| title_short | Numerical Analysis for a Fractional Differential Time-Delay Model of HIV Infection of CD4+ T-Cell Proliferation under Antiretroviral Therapy |
| title_sort | numerical analysis for a fractional differential time delay model of hiv infection of cd4 t cell proliferation under antiretroviral therapy |
| url | http://dx.doi.org/10.1155/2014/291614 |
| work_keys_str_mv | AT yiliangliu numericalanalysisforafractionaldifferentialtimedelaymodelofhivinfectionofcd4tcellproliferationunderantiretroviraltherapy AT peifenlu numericalanalysisforafractionaldifferentialtimedelaymodelofhivinfectionofcd4tcellproliferationunderantiretroviraltherapy AT ivanszanto numericalanalysisforafractionaldifferentialtimedelaymodelofhivinfectionofcd4tcellproliferationunderantiretroviraltherapy |