A Fuzzy Delay Approach for HIV Dynamics Using a Cellular Automaton
The objective of this research is to study the evolution of CD4+ T lymphocytes infected with HIV in HIV-seropositive individuals under antiretroviral treatment utilizing a mathematical model consisting of a system of delay-differential equations. The infection rate of CD4+ T lymphocytes is a time-de...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2015/378753 |
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| Summary: | The objective of this research is to study the evolution of CD4+ T lymphocytes
infected with HIV in HIV-seropositive individuals under antiretroviral treatment
utilizing a mathematical model consisting of a system of delay-differential equations. The infection rate of CD4+ T lymphocytes is a time-dependent parameter
with delay. Such delay is given by a fuzzy number due to the uncertainty of the
effects of both pharmacological and intracellular delays. A cellular automaton is
utilized to estimate the parameters of the system. The effects of antiretroviral therapy in the cellular automaton are modeled using a fuzzy rule-based system with
two inputs: the medication potency and the treatment adhesion for three hypothetical individuals. For each of them, we determine the infection rate of CD4+ T
lymphocytes, which is different from zero, as opposed to other studies reported in
the literature. As the infection rate is considered a fuzzy parameter, we determine the
fuzzy and the defuzzified solutions for the infected CD4+ T lymphocytes. We obtain the maximum values of infected cells for individuals that receive low, medium,
and high potency medication and treatment adhesion. The results obtained are in
accordance qualitatively with what would be expected in a real situation. |
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| ISSN: | 1110-757X 1687-0042 |