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

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)].

[1]  F. A. B. Coutinho,et al.  Modelling the natural history of HIV infection in individuals and its epidemiological implications , 2001, Bulletin of mathematical biology.

[2]  Hamid Ez-Zahraouy,et al.  Dynamics of HIV infection on 2D cellular automata , 2003 .

[3]  R. Bassanezi,et al.  The SI epidemiological models with a fuzzy transmission parameter , 2003 .

[4]  M. Nowak.  The Mathematical Biology of Human Infections , 1999 .

[5]  E. H. Mamdani,et al.  Advances in the linguistic synthesis of fuzzy controllers , 1976 .

[6]  R. M. Zorzenon dos Santos,et al.  Dynamics of HIV infection: a cellular automata approach. , 2001, Physical review letters.

[7]  R. M. Jafelice,et al.  Fuzzy modeling in symptomatic HIV virus infected population , 2004, Bulletin of mathematical biology.

[8]  Ebrahim H. Mamdani,et al.  An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller , 1999, Int. J. Hum. Comput. Stud..

[9]  Peter M. A. Sloot,et al.  Cellular Automata Model of Drug Therapy for HIV Infection , 2002, ACRI.

[10]  Claude H. Moog,et al.  Clinical Tests of Therapeutical Failures Based on Mathematical Modeling of the HIV Infection , 2008, IEEE Transactions on Automatic Control.

[11]  Roman M. Zaritski,et al.  Feedback-mediated dynamics in two coupled nephrons , 2004, Bulletin of mathematical biology.

[12]  Ruben A. Filter,et al.  Dynamic HIV/AIDS parameter estimation with application to a vaccine readiness study in Southern Africa , 2005, IEEE Transactions on Biomedical Engineering.

[13]  Giovanni Colombo,et al.  A non-stochastic approach for modeling uncertainty in population dynamics , 1998 .

[14]  D Commenges,et al.  Practical Identifiability of HIV Dynamics Models , 2007, Bulletin of mathematical biology.

[15]  G B Ermentrout,et al.  Cellular automata approaches to biological modeling. , 1993, Journal of theoretical biology.

[16]  W. Pedrycz,et al.  An introduction to fuzzy sets : analysis and design , 1998 .

[17]  Alan S. Perelson,et al.  Mathematical Analysis of HIV-1 Dynamics in Vivo , 1999, SIAM Rev..

[18]  Fernando Gomide,et al.  Methodology To Determine The Evolution Of Asymptomatic Hiv Population Using Fuzzy Set Theory , 2005, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[19]  Ras B. Pandey,et al.  A computer simulation study of cell population in a fuzzy interaction model for mutating HIV , 1998 .

[20]  N. Rashevsky,et al.  Mathematical biology , 1961, Connecticut medicine.

[21]  M A Caetano,et al.  A comparative evaluation of open loop and closed loop drug administration strategies in the treatment of AIDS. , 1999, Anais da Academia Brasileira de Ciencias.

[22]  Feng Lin,et al.  A Self-Learning Fuzzy Discrete Event System for HIV/AIDS Treatment Regimen Selection , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[23]  M. Nowak,et al.  Population Dynamics of Immune Responses to Persistent Viruses , 1996, Science.

[24]  Eduardo Massad,et al.  Fuzzy gradual rules in epidemiology , 2003 .