This new advanced text/reference book presents compartmental models or flow models from an applications perspective. Flow models are used when there is a flow of information or materials, such as fluid of money or energy between the components of a system. They are widely used in biomedicine but have also useful applications in studying ecosystems, input-output analysis, competition, models, and epidemology. In order to provide a complete and balanced presentation, the book is organized in four parts. Part 1 is devoted to the theory of digraphs; Part 2 addresses Markov chains; Part 3 discusses differential equations; and Part 4 presents the theory of compartmental models, addressing the relations between dynamics of the solution and structure of the model. Key applications discussed include ecosystem models, fluid transfer, competition models, tracer kinetic experiments, and network flows. Essential topics and methods are presented in an accessible style with many examples: directed graphs, differential equations, Markov chains, and compartmental model construction. The material provides a thorough and comprehensive presentation of compartmental models, model construction and applications. All advanced students, practitioners and professionals in bioscience and applied mathematical modeling will find the book a useful and excellent reference.
Introducation and simple examples. Part 1 Structure of models - directed graphs: diagraphs and graphs; a little simple graph theory; orientation of graphs and diagraphs; tournaments; planer graphs; graphs and matrices. Part 2 Diagraphs and probabilities - Markov chains: introduction to Markov chains; classification of Markov chains; regular Markov chains; absorbing Maarkov chains; from Markov chains to compartmental models. Part 3 Compartmental models - applications: introduction to compartmental models; models for the spread of epidemics; three traditional examples of compartmental models; ecosystem models; fisheries models; drug kinetics. Part 4 Compartmental model theory: basic properties of linear models; structure and dynamical properties; identifiability of a compartmental system; parameter estimation; complexity and stability.
Series: Modeling and Simulation in Science, Engineering and Technology
Number Of Pages: 250
Published: 20th September 1999
Publisher: SPRINGER VERLAG GMBH
Country of Publication: US
Dimensions (cm): 22.86 x 15.24
Weight (kg): 0.58