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数理解析研究所講究録 第 1663 巻 2009 年 20-29 20 感染症個体群動態に関する時間離散モデルについての考察 Some Remarks on Time-Discrete Models for the Epidemic Population Dynamics 瀬野裕美 広島大学大学院理学研究科数理分子生命理学専攻 Hiromi SENO Department of Mathematical and Life Sciences, Graduate School of Science, Hiroshima University, Higashi-hiroshima 739-8526 JAPAN seno@math.sci.hiroshima-u.ac.jp In this work, we present away of building atime-discrete mode], especially related to the epidemic population $?r\epsilon t$ dynamics, making use of the Royama’s kamework $[$ 4, 5, $6],which$ is sometimes called the -principle’ modelling, and further we analyze the derived discrete model to make some $compari\infty n$ to some typical ordinary di?erential equation models. Especially let us consider an epidemic population dynamioe of nonfatal disease transmission, assuming that the total population size can be regarded as constant, say $N$ , according to the epidemic time scale. We assume the probability $P_{k}(i)$ that the number of contacts to other individuals by an individual is $i$ in the $k$ th day, and give the probability that the individual who contacts in $j$ times to some infectivae in the $k$ th day successfully escapes $bom$ the infection by $(1-\beta_{k})^{j}(0\beta_{k}1)$ . We show that our discrete model has the nature mathematically analogous to that of $Kermack-McKendrick$ model if we assume that $P_{k}(i)$ follows aPoisson distribution. FUrthermore, wi