HIV Viral Dynamic under Treatment with Intracellular Delay and Virus Decay as Interactive Parameters

R. A. C. Prata, R. S. M. Jafelice, V. M. Cabral, F. S. Pedro, L. C. Barros


Treatment with antiviral drugs for human immunodeficiency virus type 1 (HIV-1) infection causes a rapid reduction in plasma viral load. Viral decline occurs in several stages and provides information on important kinetic constants of virus replication in vivo and pharmacodynamic properties. We present a mathematical model that not only considers the intracellular phase of the viral life cycle, defined as the time between the infection of a cell and the production of new viral particles, but we  also consider that this parameter together with the virus decay are interactive fuzzy numbers.


Joint possibility distribution; interactive fuzzy numbers; HIV model; Viral dynamics;

Full Text:



J. E. Mittler, B. Sulzer, A. U. Neumann, and A. S. Perelson, “Influence of

delayed viral production on viral dynamics in hiv-1 infected patients,” Mathematical biosciences, vol. 152, no. 2, pp. 143–163, 1998.

A. Herz, S. Bonhoeffer, R. M. Anderson, R. M. May, and M. A. Nowak, “Viral

dynamics in vivo: limitations on estimates of intracellular delay and virus decay,” Proceedings of the National Academy of Sciences, vol. 93, no. 14, pp. 7247–7251, 1996.

L. C. Barros, R. C. Bassanezi, and W. A. Lodwick, A First Course in Fuzzy

Logic, Fuzzy Dynamical Systems, and Biomathematics, vol. 347 of Studies in Fuzziness and Soft Computing. Springer, 1 ed., 2017.

C. Carlsson, R. Fullér, et al., “Additions of completely correlated fuzzy numbers,” in Fuzzy Systems, 2004. Proceedings. 2004 IEEE International Conference on, vol. 1, pp. 535–539, IEEE, 2004.

V. Cabral and L. C. Barros, “Fuzzy differential equation with completely correlated parameters,” Fuzzy Sets and Systems, vol. 265, pp. 86–98, 2015.

F. Santo Pedro, L. C. de Barros, and E. Esmi, “Population growth model via

interactive fuzzy differential equation,” Information Sciences, vol. 481, pp. 160–173, 2019.

R. Fullér and P. Majlender, “On interactive fuzzy numbers,” Fuzzy Sets and

Systems, vol. 143, no. 3, pp. 355–369, 2004.

A. S. Perelson, A. U. Neumann, M. Markowitz, J. M. Leonard, and D. D. Ho, “Hiv-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time,” Science, vol. 271, no. 5255, pp. 1582–1586, 1996.

R. M. Jafelice, L. Barros, and R. Bassanezi, “Study of the dynamics of hiv under treatment considering fuzzy delay,” Computational and Applied Mathematics, vol. 33, no. 1, pp. 45–61, 2014.

V. M. Cabral, R. A. C. Prata, and L. C. Barros, “f-correlated fuzzy numbers

applied to hiv model with protease inhibitor therapy,” Mathware & soft

computing, vol. 22, no. 1, pp. 46–51.

E. Massad, N. R. S. Ortega, L. C. de Barros, and C. J. Struchiner, Fuzzy logic in action: applications in epidemiology and beyond, vol. 232. Springer Science & Business Media, 2009.

O. A. d. Barros, “Estimaçao dos parâmetros da distribuiçao beta bivariada:

aplicaçoes em severidade de doenças em plantas,” Master’s thesis, Universidade de São Paulo, 2015.


Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM


  • There are currently no refbacks.

Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)


Indexed in:



Desenvolvido por:

Logomarca da Lepidus Tecnologia