Computational and Applied Mathematics

, Volume 33, Issue 1, pp 45-61

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 HIV-positive 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 rule-based system in Jafelice et al. (Bull Math Biol 66:1463–1942, 2004). Two inference methods were adopted: Mamdani and Takagi-Sugeno. 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 Takagi-Sugeno method is closer to the deterministic solution than the one obtained using Mamdani method.


Delay differential equation HIV dynamics Fuzzy delay Mamdani inference method Takagi-Sugeno inference method

Mathematics Subject Classification