翻訳と辞書 Words near each other ・ Kerling-lès-Sierck ・ Kerlingarfjöll ・ Kerlly Real ・ Kerlon ・ Kerlouan ・ KERM ・ Kerm ・ Kerm-e Kuh ・ Kerm-e Zard ・ Kerma ・ Kerma (disambiguation) ・ Kerma (physics) ・ Kerma Basin ・ Kerma Culture ・ Kermac Macmaghan ・ Kermack–McKendrick theory ・ Kermadec ・ Kermadec Islands ・ Kermadec petrel ・ Kermadec Plate ・ Kermadec rattail ・ Kermadec red-crowned parakeet ・ Kermadec scalyfin ・ Kermadec Trench ・ Kermadec triplefin ・ Kermadec-Tonga subduction zone ・ Kermadecia ・ Kermadecia pronyensis ・ Kermajan ・ Kermajan Rural District Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Kermack–McKendrick theory ： ウィキペディア英語版 Kermack–McKendrick theory Kermack–McKendrick theory is a mathematical hypothesis about how infectious diseases spread through a population. Building on the research of Ronald Ross and others, A. G. McKendrick and W. O. Kermack published their theory in a set of three articles from 1927, 1932, and 1933. While Kermack—McKendrick theory was indeed the source of SIR models and their relatives, Kermack and McKendrick were thinking of a more subtle and empirically useful problem than the simple compartmental models discussed here. The text is somewhat difficult to read, compared to modern papers, but the important feature is it was a model where the age-of-infection affected the transmission and removal rates. Because of their seminal importance to the field of theoretical epidemiology, these articles were republished in the ''Bulletin of Mathematical Biology'' in 1991. == Epidemic model (1927) == In its initial form, Kermack—McKendrick theory is a compartmental differential-equation model that structures the infectioned population in terms of age-of-infection, while using simple compartments for people who are susceptible (S) and recovered/removed (R). Specified initial conditions would change over time according to : $\backslash frac\; =\; -\; \backslash lambda\; S,$ : $\backslash frac\; +\; \backslash frac\; =\; \backslash delta(a)\; \backslash lambda\; S-\; \backslash gamma(a)\; i,$ : $\backslash frac\; =\; \backslash int\_^\backslash infty\; \backslash gamma(a)\; i(a,t)\; \backslash ,\; da\; ,$ where $\backslash delta(a)$ is a Dirac delta-function and the infection pressure : $\backslash lambda\; =\; \backslash int\_0^\backslash infty\; \backslash beta(a)\; i(a,t)\; \backslash ,\; da\; .$ Only in the special case when the removal rate $\backslash gamma(a)$ and the transmission rate $\backslash beta(a)$ are constant for all ages does the substitution $I(t)\; =\; \backslash int\_0^\backslash infty\; i(a,t)\; \backslash ,\; da$ transform their theory into the simple SIR model. This basic model only accounts for infection and removal events, which are sufficient to describe a simple epidemic, including the threshold condition necessary for an epidemic to start, but can not explain endemic disease transmission or recurring epidemics. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Kermack–McKendrick theory」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.