Simulación basada en SMA de sistemas originalmente representados con EDO

En el presente trabajo se expone una metodologia para modelar mediante un Sistema Multi-Agente (SMA) sistemas biologicos y fisiologicos dinamicos con variables cuantificadas discretas, como el crecimiento y decrecimiento de poblaciones o el modelado epidemiologico de enfermedades. Se muestra un procedimiento para transformar un sistema de Ecuaciones Diferenciales Ordinarias (EDO) (que modela un entorno de forma correcta) en un SMA equivalente mediante un esquema basado en el metodo de Monte Carlo. Se utiliza un caso practico fundamentado en un modelo matematico de Leucemia Mieloide Cronica (LMC) para comparar la metodologia basada en agentes con el modelado tradicional basado en un sistema de EDO. Se realiza una simulacion con cada modelo (SMA y EDO) y se compara los resultados obtenidos con ambas metodologias.

[1]  B. Øksendal.  Stochastic differential equations : an introduction with applications , 1987 .

[2]  Soumya Banerjee,et al.  Artificial Immune Systems, 8th International Conference, ICARIS 2009, York, UK, August 9-12, 2009. Proceedings , 2009, ICARIS.

[3]  Sebastian Bohl,et al.  Computational processing and error reduction strategies for standardized quantitative data in biological networks , 2005, The FEBS journal.

[4]  Dongfang Wu,et al.  Unbiased estimation of Weibull parameters with the linear regression method , 2006 .

[5]  S. Spencer,et al.  An ordinary differential equation model for the multistep transformation to cancer. , 2004, Journal of theoretical biology.

[6]  P Gennemark,et al.  Efficient algorithms for ordinary differential equation model identification of biological systems. , 2007, IET systems biology.

[7]  Michael Wooldridge,et al.  Introduction to multiagent systems , 2001 .

[8]  Stephen M. Krone,et al.  Analyzing animal movements using Brownian bridges. , 2007, Ecology.

[9]  François Bousquet,et al.  Multi-agent systems in epidemiology: a first step for computational biology in the study of vector-borne disease transmission , 2008, BMC Bioinformatics.

[10]  Jacques Ferber,et al.  Environments for Multiagent Systems State-of-the-Art and Research Challenges , 2004, E4MAS.

[11]  Jay X. Tang,et al.  Amplified effect of Brownian motion in bacterial near-surface swimming , 2008, Proceedings of the National Academy of Sciences.

[12]  J. Nagy.  Competition and natural selection in a mathematical model of cancer , 2004, Bulletin of mathematical biology.

[13]  Joc Cing Tay,et al.  A hybrid agent-based approach for modeling microbiological systems. , 2008, Journal of theoretical biology.

[14]  A. Marciniak-Czochra,et al.  Mathematical modelling of the influence of heat shock proteins on cancer invasion of tissue , 2009, Journal of mathematical biology.

[15]  David R. Gilbert,et al.  A Model Checking Approach to the Parameter Estimation of Biochemical Pathways , 2008, CMSB.

[16]  Svetlana Bunimovich-Mendrazitsky,et al.  Mathematical Model of Pulsed Immunotherapy for Superficial Bladder Cancer , 2008, Bulletin of mathematical biology.

[17]  Awad El-Gohary,et al.  The chaos and optimal control of cancer model with complete unknown parameters , 2009 .

[18]  M. Meyer-Hermann.  AGENT-BASED MODELS OR DIFFERENTIAL EQUATIONS: TWO WAYS TO LEARN ABOUT SELECTION MECHANISMS IN GERMINAL CENTRES , 2008 .

[19]  Ronald W. Shonkwiler.  Mathematical Biology: An Introduction with Maple and Matlab , 2009 .

[20]  Yves Demazeau,et al.  Multi-Agent Architecture Integrating Heterogeneous Models of Dynamical Processes: The Representation of Time , 1998, MABS.

[21]  Ronald L. Wasserstein,et al.  Monte Carlo: Concepts, Algorithms, and Applications , 1997 .

[22]  Klaus Schittkowski,et al.  Numerical Data Fitting in Dynamical Systems: A Practical Introduction with Applications and Software , 2002 .

[23]  Vincent Rodin,et al.  Reaction-Agents: First Mathematical Validation of a Multi-agent System for Dynamical Biochemical Kinetics , 2005, EPIA.

[24]  Jacques Ferber,et al.  Multi-agent systems - an introduction to distributed artificial intelligence , 1999 .

[25]  Paolo Ubezio,et al.  A Generalised Age- and Phase-Structured Model of Human Tumour Cell Populations Both Unperturbed and Exposed to a Range of Cancer Therapies , 2007, Bulletin of mathematical biology.

[26]  Danny Weyns,et al.  Exploiting a Virtual Environment in a Real-World Application , 2005, E4MAS.

[27]  J. Murray.  Models for Interacting Populations , 1993 .

[28]  Helen Moore,et al.  A mathematical model for chronic myelogenous leukemia (CML) and T cell interaction. , 2004, Journal of theoretical biology.

[29]  P. Ramírez,et al.  Leucemia mieloide crónica: Actualización en Citogenética y Biología Molecular , 2005 .