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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Next-generation matrix ： ウィキペディア英語版 Next-generation matrix In epidemiology, the next-generation matrix is a method used to derive the basic reproduction number, for a compartmental model of the spread of infectious diseases. This method is given by Diekmann ''et al.'' (1990) and van den Driessche and Watmough (2002). To calculate the basic reproduction number by using a next-generation matrix, the whole population is divided into $n$ compartments in which there are :$\backslash frac=\; F\_i\; (x)-V\_i(x)$, where $V\_i(x)=\; ()$ In the above equations, $F\_i(x)$ represents the rate of appearance of new infections in compartment $i$. $V^+\_i$ represents the rate of transfer of individuals into compartment $i$ by all other means, and $V^-\_i\; (x)$ represents the rate of transfer of individuals out of compartment $i$. The above model can also be written as : $\backslash frac=\; F(x)-V(x)$ where : $F(x)\; =\; \backslash begin$ F_1(x), & F_2(x), & \ldots, & F_n(x) \end^T and : $V(x)\; =\; \backslash begin$ V_1(x), & V_2 (x), & \ldots, & V_n(x) \end^T. Let $x\_0$ be the disease-free equilibrium. The values of the Jacobian matrices $F(x)$ and $V(x)$ are: : $DF(x\_0)\; =\; \backslash begin$ F & 0 \\ 0 & 0 \end and : $$ DV(x_0) = \begin V & 0 \\ J_3 & J_4 \end respectively. Here, $F$ and $V$ are ''m'' × ''m'' matrices, defined as $F=\; \backslash frac(x\_0)$ and $V=\backslash frac(x\_0)$. Now, the matrix $FV^$ is known as the next-generation matrix. The largest eigenvalue or spectral radius of $FV^$ is the basic reproduction number of the model. ==See also== *Mathematical modelling of infectious disease 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「Next-generation matrix」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.