存続と絶滅の数理

概要

論文の詳細を見る
In this survey, we introduce the relatively new mathematical idea "permanence" which implies robust coexistence for all elements (that is, the species or cells et al.) of the biological systems. During last two decades, analytical method to prove permanence as well as the idea itself has been rapidly developed. Also the study on permanence proves its importance both for mathematicians and biologists to cooperate together. That is, it has proposed many interesting mathematical problems and stimulated to acquire new mathematical ideas. Simultaneously, it gave the deep understanding of the biological world. First, we sketch some history on permanence and give the similar framework of the models for epidemics, HIV, autoimmune. Next, we survey the results on permanence for ODE models with or without time delays. We argue also average extinction time for some stochastic process. We gave many references including some Japanese books for the readers who are interested in mathematics on permanence.
日本応用数理学会の論文
2006-12-26