Stochastic population models. A compartmental perspective
type: Item
instance of: scholarly article
title: Stochastic population models. A compartmental perspective
zbMATH Open document ID: 0943.92029
author: James H. Matis
author: Thomas R. Kiffe
published in: Lecture Notes in Statistics
publication date: 2000-07-24T00:00:00Z
review text: Mathematical models are useful in formulating and refining hypotheses about biological processes and have attracted considerable amount of research efforts [see, e.g., \textit{R.B. Banks}, Growth and diffusion phenomena. Mathematical frameworks and applications. (1994; Zbl 0788.92001); \textit{J.A. Jacquez}, Compartmental analysis in biology and medicine. (1996; Zbl 0703.92001); \textit{E. Renshaw}, Modelling biological populations in space and time. (1991; Zbl 0754.92018); \textit{D.H. Anderson}, Compartmental modeling and tracer kinetics. (1983; Zbl 0509.92001)]. This book presents a unified treatment of stochastic discrete population-growth models. The authors develop models which not only describe but also explain changes in populations. Most of the models of interest are sets of differential equations, where the underlying parameters are related to the kinetics of the process. These kinetic models could be used to analyze population data, to make statistical inferences and to predict population size. Some of these models are quite sophisticated and incorporate detailed mechanistic concepts. The monograph focuses on the development of exact and approximate solutions for analogous stochastic models based on birth-death-migration processes. The models are illustrated with numerous practical applications. The monograph consists of three parts with a total of 14 chapters. The first part presents an overview and applications to four real world problems, viz., invasion of Africanized honey bees, Muskrat spread in the Netherlands, Bioaccumulation of mercury in fish and human calcium kinetics. The second part describes stochastic birth-death models for the growth of a single population. It develops new insights for nonlinear population models by employing an effective cumulant approach. The last part employs multi-dimensional birth-death-migration models for describing biological spread through a stochastic compartmental analysis. The development of stochastic linear mu…
reviewed by: P. R. Parthasarathy
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 92-02
Mathematics Subject Classification ID: 60J85
Mathematics Subject Classification ID: 92D40
zbMATH DE Number: 1480162
zbMATH Keywords: birth-death models
zbMATH Keywords: cumulants
zbMATH Keywords: host-parasite model
describes a project that uses: Mathematica
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1480162