Analysis of HIV models with two time delays
Time delays can affect the dynamics of HIV infection predicted by mathematical models. In this paper, we studied two mathematical models each with two time delays. In the first model with HIV latency, one delay is the time between viral entry into a cell and the establishment of HIV latency, and the...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2017-03-01
|
| Series: | Journal of Biological Dynamics |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/17513758.2016.1148202 |
| _version_ | 1819078069285027840 |
|---|---|
| author | Areej Alshorman Xia Wang M. Joseph Meyer Libin Rong |
| author_facet | Areej Alshorman Xia Wang M. Joseph Meyer Libin Rong |
| author_sort | Areej Alshorman |
| collection | DOAJ |
| description | Time delays can affect the dynamics of HIV infection predicted by mathematical models. In this paper, we studied two mathematical models each with two time delays. In the first model with HIV latency, one delay is the time between viral entry into a cell and the establishment of HIV latency, and the other delay is the time between cell infection and viral production. We defined the basic reproductive number and showed the local and global stability of the steady states. Numerical simulations were performed to evaluate the influence of time delays on the dynamics. In the second model with HIV immune response, one delay is the time between cell infection and viral production, and the other delay is the time needed for the adaptive immune response to emerge to control viral replication. With two positive delays, we obtained the stability crossing curves for the model, which were shown to be a series of open-ended curves. |
| first_indexed | 2024-12-21T19:07:14Z |
| format | Article |
| id | doaj.art-4b53e95d4cc74358ae59db6be45cf9cd |
| institution | Directory Open Access Journal |
| issn | 1751-3758 1751-3766 |
| language | English |
| last_indexed | 2024-12-21T19:07:14Z |
| publishDate | 2017-03-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Biological Dynamics |
| spelling | doaj.art-4b53e95d4cc74358ae59db6be45cf9cd2022-12-21T18:53:19ZengTaylor & Francis GroupJournal of Biological Dynamics1751-37581751-37662017-03-01110406410.1080/17513758.2016.11482021148202Analysis of HIV models with two time delaysAreej Alshorman0Xia Wang1M. Joseph Meyer2Libin Rong3Oakland UniversityXinyang Normal UniversityOakland UniversityOakland UniversityTime delays can affect the dynamics of HIV infection predicted by mathematical models. In this paper, we studied two mathematical models each with two time delays. In the first model with HIV latency, one delay is the time between viral entry into a cell and the establishment of HIV latency, and the other delay is the time between cell infection and viral production. We defined the basic reproductive number and showed the local and global stability of the steady states. Numerical simulations were performed to evaluate the influence of time delays on the dynamics. In the second model with HIV immune response, one delay is the time between cell infection and viral production, and the other delay is the time needed for the adaptive immune response to emerge to control viral replication. With two positive delays, we obtained the stability crossing curves for the model, which were shown to be a series of open-ended curves.http://dx.doi.org/10.1080/17513758.2016.1148202HIV infectionlatencyimmune responsecharacteristic quasipolynomialstabilitystability crossing curve |
| spellingShingle | Areej Alshorman Xia Wang M. Joseph Meyer Libin Rong Analysis of HIV models with two time delays Journal of Biological Dynamics HIV infection latency immune response characteristic quasipolynomial stability stability crossing curve |
| title | Analysis of HIV models with two time delays |
| title_full | Analysis of HIV models with two time delays |
| title_fullStr | Analysis of HIV models with two time delays |
| title_full_unstemmed | Analysis of HIV models with two time delays |
| title_short | Analysis of HIV models with two time delays |
| title_sort | analysis of hiv models with two time delays |
| topic | HIV infection latency immune response characteristic quasipolynomial stability stability crossing curve |
| url | http://dx.doi.org/10.1080/17513758.2016.1148202 |
| work_keys_str_mv | AT areejalshorman analysisofhivmodelswithtwotimedelays AT xiawang analysisofhivmodelswithtwotimedelays AT mjosephmeyer analysisofhivmodelswithtwotimedelays AT libinrong analysisofhivmodelswithtwotimedelays |