Stochastic Population and Epidemic Models: Persistence and Extinction
暫譯: 隨機人口與流行病模型：持續性與滅絕

Allen, Linda J. S.

Stochastic Population and Epidemic Models: Persistence and Extinction

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商品描述

This monograph provides a summary of the basic theory of branching processes for single-type and multi-type processes. Classic examples of population and epidemic models illustrate the probability of population or epidemic extinction obtained from the theory of branching processes. The first chapter develops the branching process theory, while in the second chapter two applications to population and epidemic processes of single-type branching process theory are explored. The last two chapters present multi-type branching process applications to epidemic models, and then continuous-time and continuous-state branching processes with applications. In addition, several MATLAB programs for simulating stochastic sample paths are provided in an Appendix.

These notes originated as part of a lecture series on Stochastics in Biological Systems at the Mathematical Biosciences Institute in Ohio, USA.

Professor Linda Allen is a Paul Whitfield Horn Professor of Mathematics in the Department of Mathematics and Statistics at Texas Tech University, USA.

商品描述(中文翻譯)

這本專著提供了單一類型和多類型分支過程的基本理論摘要。經典的人口和流行病模型示例說明了從分支過程理論中獲得的人口或流行病滅絕的概率。第一章發展了分支過程理論，而第二章則探討了單一類型分支過程理論在人口和流行病過程中的兩個應用。最後兩章介紹了多類型分支過程在流行病模型中的應用，然後是連續時間和連續狀態的分支過程及其應用。此外，附錄中提供了幾個用於模擬隨機樣本路徑的 MATLAB 程式。

這些筆記源於美國俄亥俄州數學生物科學研究所的生物系統隨機過程講座系列。

琳達·艾倫教授是美國德克薩斯科技大學數學與統計系的保羅·惠特菲爾德·霍恩數學教授。

作者簡介

Linda J. S. Allen is a Professor in the Department of Mathematics and Statistics at Texas Tech University. Allen's primary research interest is mathematical modeling in biology. She formulates and analyzes deterministic and stochastic models in describing population, epidemic, viral and immune-system dynamics.

作者簡介(中文翻譯)

琳達·J·S·艾倫（Linda J. S. Allen）是德克薩斯科技大學（Texas Tech University）數學與統計系的教授。艾倫的主要研究興趣是生物學中的數學建模。她在描述人口、流行病、病毒和免疫系統動態方面，制定和分析確定性及隨機模型。

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