| Title:
|
On the global dynamics of the cancer AIDS-related mathematical model (English) |
| Author:
|
Starkov, Konstantin E. |
| Author:
|
Plata-Ante, Corina |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
50 |
| Issue:
|
4 |
| Year:
|
2014 |
| Pages:
|
563-579 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we examine some features of the global dynamics of the four-dimensional system created by Lou, Ruggeri and Ma in 2007 which describes the behavior of the AIDS-related cancer dynamic model in vivo. We give upper and lower ultimate bounds for concentrations of cell populations and the free HIV-1 involved in this model. We show for this dynamics that there is a positively invariant polytope and we find a few surfaces containing omega-limit sets for positive half trajectories in the positive orthant. Finally, we derive the main result of this work: sufficient conditions of ultimate cancer free behavior. (English) |
| Keyword:
|
cancer growth model |
| Keyword:
|
AIDS |
| Keyword:
|
compact invariant set |
| Keyword:
|
omega-limit set |
| Keyword:
|
localization |
| Keyword:
|
ultimate cancer free dynamics |
| MSC:
|
34C11 |
| MSC:
|
34D23 |
| MSC:
|
92D25 |
| MSC:
|
92D30 |
| MSC:
|
93D20 |
| idZBL:
|
Zbl 06386427 |
| idMR:
|
MR3275085 |
| DOI:
|
10.14736/kyb-2014-4-0563 |
| . |
| Date available:
|
2014-11-06T15:01:39Z |
| Last updated:
|
2016-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143984 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
[18] Valle, P. A., Coria, L. N., Starkov, K. E.: Estudio de la dinamica global para un modelo de evasion-inmune de un tumor cancerigeno..Comp. y Sistemas, accepted. |
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|
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| . |
