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 C D 4 + 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. Thiébaut, 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)].