Compartmental modeling with networks
The flow models, used in biomedicine for tracer experiments, in biology e.g. for the study of ecosystems, as well as in input-output analysis in economics, arms races, and in the study of epidemics, are usually called compartmental models to distinguish them from diffusion models. To construct them, a system is divided into homogeneous compartments and the flows of material between the various compartments and to and from the outside are traced. The aim of this monograph is to present these models and their applications. This involves consideration of some properties of digraphs, their relations to systems of differential equations and their conversion to Markov chains. The book is organized in four parts. The first part is devoted to the theory of digraphs. The second part deals with Markov chains. The third part introduces the differential equations associated with compartmental models and develops their theory to some extent. The final part goes into the theory of compartmental models, where the relations between the dynamics of the solutions and the structure of the model is studied. In the Appendix, some mathematical prerequisites such as matrix operations, finding eigenvectors, systems of differential equations and matrices with Maple, are given.
scientific article; zbMATH DE number 1345951