Modeling the Dynamics of HIV Infection with Conformon-P Systems and Cellular Automata
Further results on the study of the dynamics of HIV infection with grids of conformon-P systems are reported. This study clearly shows a subdivision in two phases of the mechanism at the base of the considered dynamics.
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Abstract. Further results on the study of the dynamics of HIV infection with grids of conformon-P systems are reported. This study clearly shows a subdivision in two phases of the mechanism at the base of the considered dynamics.
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Introduction
The infection by the human immune-deficiency virus (HIV), the cause of acquired immunodeficiency syndrome (AIDS), has been widely studied both in the laboratory and with computer models in order to understand the different aspects that regulate the virus-host interaction. Several mathematical models have been proposed (see, for example, [14,18,11]) but all of them fail to describe some aspects of the infection. The recent model reported by Dos Santos & Coutinho in [4], based on cellular automata (CA), clearly shows the different time scales of the infection and has a broad qualitative agreement to the density of healthy and infected cells observed in vivo. However, in [15] it is noted that this qualitative agreement is reached only if some parameters are chosen in a small interval. If some of the parameters are chosen outside this interval, then the cellular automata model of [4] does not follow the dynamics of what is observed in vivo. In the present paper we continue our study on the modeling of the dynamics of HIV infection with grids of conformon-P systems started in [2]. There our model proved to be more robust than the CA model to a wide range of conditions and parameters, with more reproducible qualitative agreement to the overall dynamics and to the densities of healthy and infected cells observed in vivo.
2 2.1
The Modeling Platforms Cellular Automata
Cellular automata are a regularly used platform for modeling, and are increasingly explored as modeling tools in the context of natural phenomena that exhibit characteristic spatiotemporal dynamics [16,3]. Of interest here, for example, are their use in modeling the spread of infection [1,12,4,11,17]. G. Eleftherakis et al. (Eds.): WMC8 2007, LNCS 4860, pp. 21–31, 2007. c Springer-Verlag Berlin Heidelberg 2007
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P. Frisco and D.W. Corne
A CA consists of a finite number of cells (invariably arranged in a regular spatial grid), each of which can be in one of a finite (typically small) number of specific states. In the usual approach, at each time step t the status of the CA is characterized by its state vector; that is, the state of each of the cells. In the simplest type of CA, the state vector at time t+ 1 is obtained from that at time t by the operation of a single rule applied in parallel (synchronously) to each cell. The rule specifies how the state of a cell will change as a function of its current state and the states of the cells in its neighborhood (see Figure 4). In many applications, including that addressed here, it is appropriate for the rule to be probabilistic. The straightforward nature of the time evolution of a CA, combined with its emphasis on local interactions, has made it an accessible and attractive tool for modeling many biological processes. 2.2
Conformon-P Systems
Conformon-P systems (cP
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