Stochastic Processes and Applications in Biology and Medicine II: Models(4 Biomathematics)

This volume is a revised and enlarged version of Chapter 3 of. a book with the same title, published in Romanian in 1968. The revision resulted in a new book which has been divided into two of the large amount of new material. The whole book parts because is intended to introduce mathematicians and biologists with a strong mathematical background to the study of stochastic processes and their applications in biological sciences. It is meant to serve both as a textbook and a survey of recent developments. Biology studies complex situations and therefore needs skilful methods of abstraction. Stochastic models, being both vigorous in their specification and flexible in their manipulation, are the most suitable tools for studying such situations. This circumstance deter- mined the writing of this volume which represents a comprehensive cross section of modern biological problems on the theory of stochastic processes. Because of the way some specific problems have been treat- ed, this volume may also be useful to research scientists in any other field of science, interested in the possibilities and results of stochastic modelling. To understand the material presented, the reader needs to be acquainted with probability theory, as given in a sound introductory course, and be capable of abstraction.

Table of Contents:
0. Prolegomenon.- 1. Preliminary considerations.- 1.1. Stochastic and deterministic models in biology.- 1.1.1. Comparisons with deterministic models.- 1.1.2. Equipollent and conjunct models.- 1.2. The structure of biological populations.- 1.2.1. Elements of bio-logic.- 1.2.2. Distinguishability and indistinguishability.- 1.2.3. Equivalence relations and graphs.- 1.2.4. Descendants, generations and families.- 1.2.5. The temporal structure of populations and biological objects.- 1.2.6. Characteristic distributions for some biological populations.- 2. Population growth models.- 2.1. Stochastic population processes.- 2.1.1. Point processes as models of stochastic populations.- 2.1.2. Homogeneous birth-and-death processes.- 2.1.3. A random walk example.- 2.1.4. Birth, death and diffusion processes.- 2.2. Population processes in Euclidean space.- 2.2.1. Homogeneous spatial models.- 2.2.2. Birth, death and migration processes in R2 [and R3.- 2.3. Intrinsic processes.- 2.3.1. Multiple-phase processes.- 2.3.2. The life cycle process.- 2.3.3. The birth, death and marks transmission process.- 2.3.4. Interdependent (self)-replicating process.- 2.3.5. Point mutation processes.- 2.4. Stochastic demographic models.- 2.4.1. The discrete time model.- 2.4.2. A model related to human populations.- 2.4.3. Population growth of the sexes.- 2.4.4. The reproductive process.- 2.5. Other growth models and derived processes.- 2.5.1. The cumulative process.- 2.5.2. The Prendiville (logistic) process.- 2.5.3. Some problems of survival and extinction.- 3. Population dynamics processes.- 3.1. Some multi-dimensional Markov jump processes.- 3.1.1. Consael processes.- 3.1.2. A generalized w-dimensional (n ? 2) linear growth process.- 3.2. Immigration-emigration processes.- 3.2.1. The Kendall process.- 3.2.2. Immigration and emigration processes.- 3.2.3. Intermigration and colonization.- 3.2.4. Taxis and kinesis as dispersion processes.- 3.3. Competition processes.- 3.3.1. Some introductory remarks.- 3.3.2. Stochastic competition processes.- 3.3.3. Quasi-competition processes.- 3.3.4. Population excess and cannibalism.- 3.4. Poikilopoiesis models.- 3.4.1. A stochastic approach to embryogenesis.- 3.4.2. Hematopoiesis models.- 4. Evolutionary processes.- 4.1. Basic problems, models and methods.- 4.1.1. Paradigm for the stochastic evolutionary processes.- 4.1.2. Classical genetic stochastic models.- 4.1.3. Tendency to homozygosity.- 4.1.4. Diffusion approximations.- 4.1.5. Non-Mendelian situations.- 4.1.6. Direct product Galton-Watson chains.- 4.2. Random drift and systematic evolutionary processes.- 4.2.1. Random drift.- 4.2.2. Selection.- 4.2.3. Mutation.- 4.3. Problems of molecular genetics.- 4.3.1. Growing point of donor DNA attachment model.- 4.3.2. An example of a random system with complete connections.- 5. Models in physiology and pathology.- 5.1. Stochastic models in physiology.- 5.1.1. Models of the appearance and the transmission of the neural flux.- 5.1.2. Chemical mediation processes.- 5.1.3. Some problems of stochastic networks.- 5.1.4. A model of muscle contraction.- 5.1.5. Renewal processes in pharmacology.- 5.1.6. Multicompartment systems.- 5.2. Models in pathology.- 5.2.1. The process of infection.- 5.2.2. The clinical process.- 5.2.3. Stochastic models for tumour growth.- 5.2.4. Some stochastic aspects of chemotherapy.- 5.2.5. Competing risks of illness.- 5.2.6. Control of biological processes.- 5.3. Epidemic processes.- 5.3.1. The classical models.- 5.3.2. A general approach to epidemics.- 5.3.3. Epidemic Markov chains.- References.- Notation index.- Author index.