Computational and Applied Mathematics
, Volume 33, Issue 1, pp 4561
First online:
Study of the dynamics of HIV under treatment considering fuzzy delay
 R. M. JafeliceAffiliated withFaculty of Mathematics, Federal University of Uberlândia Email author
 , L. C. BarrosAffiliated withDepartment of Applied Mathematics, IMECC, State University of Campinas
 , R. C. BassaneziAffiliated withCenter of Mathematics, Computation and Cognition, Federal University of ABC
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This article describes a study of the decay dynamics of the HIV (human immunodeficiency virus) population in blood plasma in response to antiretroviral therapy of HIVpositive individuals by means of a system of delay differential equations. This delay is defined as the time elapsed between the infection of a cell by the CD4+ type T lymphocyte and the production of new virus particles. The delay is considered uncertain due the differences in the cell activation state. To study the relationship between the rate of decline in the plasma virus concentration (\(u\)) and the intracellular delay (\(\tau \)), we used a fuzzy rulebased system in Jafelice et al. (Bull Math Biol 66:1463–1942, 2004). Two inference methods were adopted: Mamdani and TakagiSugeno. The HIV decay curve, which is the solution of a system of differential equations with fuzzy distributed delay, is determined by means of Zadeh’s extension principle. Finally, centroid defuzzification is used to determine a fuzzy expected HIV decay curve. The defuzzified curve that was obtained using TakagiSugeno method is closer to the deterministic solution than the one obtained using Mamdani method.
Keywords
Delay differential equation HIV dynamics Fuzzy delay Mamdani inference method TakagiSugeno inference methodMathematics Subject Classification
34K36 Title
 Study of the dynamics of HIV under treatment considering fuzzy delay
 Journal

Computational and Applied Mathematics
Volume 33, Issue 1 , pp 4561
 Cover Date
 201404
 DOI
 10.1007/s4031401300426
 Print ISSN
 01018205
 Online ISSN
 18070302
 Publisher
 Springer Basel
 Additional Links
 Topics
 Keywords

 Delay differential equation
 HIV dynamics
 Fuzzy delay
 Mamdani inference method
 TakagiSugeno inference method
 34K36
 Authors

 R. M. Jafelice ^{(1)}
 L. C. Barros ^{(2)}
 R. C. Bassanezi ^{(3)}
 Author Affiliations

 1. Faculty of Mathematics, Federal University of Uberlândia, Uberlândia, Brazil
 2. Department of Applied Mathematics, IMECC, State University of Campinas, Campinas, Brazil
 3. Center of Mathematics, Computation and Cognition, Federal University of ABC, Santo André, Brazil