Study of the dynamics of HIV under treatment considering fuzzy delay

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)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 () and the intracellular delay (), 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.3314561Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Brazilian National Research Council [306872/2009-9]Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)CNPq [477918/2010-7]Brazilian National Research Council [306872/2009-9

Fuzzy parameters in a partial differential equation model for population dispersal of leaf-cutting ants

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)This paper proposes a model for the reoccupation of ants in a region of attraction, using evolutive partial differential diffusion-advection equations, in which the population dispersion and velocity in directions x and y are fuzzy parameters. The domain under study contains an attractive region, representing areas with high concentrations of palatable host plants with better nutritious qualities. The algorithm developed here uses information about the foraging behavior of a leaf-cutting ant colony of the Amazon region in northern Brazil. In the first model, we determined the numerical solution of the partial differential deterministic equation with constant dispersion and velocity, without incorporating uncertainties that may occur in this type of biological phenomenon. In the second model, we calculated the numerical solution of the partial differential equation, determining the dispersion at each iteration and for each triangular finite element. The dispersion was determined from a fuzzy rule-based system that depends on the number of individuals of the population and on the characteristics of the terrain. In this model, we also considered the velocity along the x and y directions as a fuzzy parameter that depends on the ant movement characteristics on the terrain in the y and x directions, respectively. The two models produced solutions consistent with ant behavior in response to the proximity of an attractive region, as stated in the papers by Shepherd (1982)[2] and Vasconcelos (1999)[3], but the fuzzy model incorporates uncertainties that do occur in the biological phenomenon under study. (C) 2011 Elsevier Ltd. All rights reserved.12633973412Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)CNPq [152068/2007-4, 477918/2010-7

Fuzzy modeling in symptomatic HIV virus infected population

This paper introduces a model for the evolution of positive HIV population and manifestation of AIDS (acquired immunideficiency syndrome). The focus is on the nature of the transference rate of HIV to AIDS. Expert knowledge indicates that the transference rate is uncertain and depends strongly on the viral load and the CD4+ level of the infected individuals. Here, we suggest to view the transference rate as a fuzzy set of the viral load and CD4+ level values. In this case the dynamic model results in a fuzzy model that preserves the biological meaning and nature of the transference rate lambda. Its behavior fits the natural history of HIV infection reported in the medical science domain. The paper also includes a comparison between the fuzzy model and a classic Anderson's model using data reported in the literature. (C) 2004 Society for Mathematical Biology. Published by Elsevier Ltd. All rights reserved.6661597162

Cellular automata with fuzzy parameters in microscopic study of positive HIV individuals

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)The aim of this paper is to introduce a model to simulate the evolution of HIV in the bloodstream of positive individuals subject to medical treatment and monitoring of the medication potency and treatment adhesion. For this purpose, a cellular automata approach coupled with fuzzy set theory is developed to study the HIV evolution. The study is conducted using two cellular automata models in two corresponding steps. The first step concerns HIV dynamics in individuals with no antiretroviral therapy. In this case, the trajectory developed by the cellular automaton model depicts all phases shown in the known history of HIV dynamics. The main purpose of the first step is to serve as a model validation step. The second step extends the model developed in the first step to consider HIV dynamics in individuals under antiretroviral therapy. The effects of antiretroviral therapy in the cellular automaton model are modeled using a fuzzy rule-based system with two inputs, the medication potency and treatment adhesion rate of the individuals to the therapy. The fuzzy rule-based system is used to compute the number of HIV infected CD4+ cells and the viral replication. The results developed by the cellular automaton model with antiretroviral therapy are close to the ones reported in the literature and agree with the behavior expected by experts [J. Guedj, R. Thiebaut, D. Commenges, Practical identifiability of HIV dynamics models, Bulletin of Mathematical Biology 69 (8) (2007) 2493-2513], [R. A. Filter, X. Xia, C. M. Gray, Dynamic HIV/AIDS parameter estimation with application to a vaccine readiness study in southern Africa, IEEE Transactions on Biomedical Engineering 52 (5) (2005) 784-791] and [D. A. Ouattara, M. J. Mhawej, C. H. Moog, Clinical tests of therapeutical failures based on mathematical modeling of the HIV infection, Systems Biology (2008) 230-241 (special issue)]. (C) 2009 Elsevier Ltd. All rights reserved.50416713244Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG)Research Foundation of the State of Minas Gerais [CEX-109/04]Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Brazilian National Research Council [152068/2007-4]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Research Foundation of the State of Sao Paulo [06/05920-7]Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Research Foundation of the State of Minas Gerais [CEX-109/04]Brazilian National Research Council [152068/2007-4]Research Foundation of the State of Sao Paulo [06/05920-7]CNPq [307890/2006-6, 304857/2006-8

HIV therapy via noncomputational optimal control approach

In this chapter, we numerically show that the dynamics of the HIV system is sensitive to both the initial condition and the system parameters. These phenomena imply that the system is chaotic and exhibits a bifurcation behavior. To control the system, we propose to initiate an HIV therapy based on both the concentration of the HIV-1 viral load and the ratio of the CD4 lymphocyte population to the CD8 lymphocyte population. If the concentration of the HIV-1 viral load is higher than a threshold, then the first type of therapy will be applied. If the concentration of the HIV-1 viral load is lower than or equal to the threshold and the ratio of the CD4 lymphocyte population to the CD8 lymphocyte population is greater than another threshold, then the second type of therapy will be applied. Otherwise, no therapy will be applied. The advantages of the proposed control strategy are that the therapy can be stopped under certain conditions, while the state variables of the overall system is asymptotically stable with fast convergent rate, the concentration of the controlled HIV-1 viral load is monotonic decreasing, as well as the positivity constraint of the system states and that of the dose concentration is guaranteed to be satisfied. Computer numerical simulation results are presented for an illustration