Library of Congress Cataloging-in-PublicationData 8tochastic epidemie models and their statistical analysis / Hâkan Andersson, Tom Britton. p. cm. --(Lecture notes in statistics; 151) Inc1udes bibliographical references and index.
A brief theoretical and methodological overview is given of the person-oriented and the variable-oriented approach, how these are commonly used in longitudinal research, and what one should take into consideration before choosing either approach. An empirical research example is also given where the association was studied between, on the one hand, attention control – activity level in early adolescence and, on the other hand, persistent versus adolescence-limited criminality. Key topics discussed include properties that variables must have to be suitable for the study of individual pattern development, the problem-method match, and prediction versus understanding.
The time until extinction for the closed SIS stochastic logistic epidemic model is investigated. We derive the asymptotic distribution for the extinction time as the population grows to infinity, under different initial conditions and for different values of the infection rate.
We consider a simple stochastic discrete-time epidemic model in a large closed homogeneous population that is not necessarily homogeneously mixing. Rather, each individual has a fixed circle of acquaintances and the epidemic spreads along this social network. In case the number of initially infective individuals stays small, a branching process approximation for the number of infectives is in force. Moreover, we provide a deterministic approximation of the bivariate process of susceptible and infective individuals, valid when the number of initially infective individuals is large. These results are used in order to derive the basic reproduction number and the asymptotic final epidemic size of the process. The model is described in the framework of random graphs.
Empirical evidence shows that childhood diseases persist in large communities whereas in smaller communities the epidemic goes extinct (and is later reintroduced by immigration). The present paper treats a stochastic model describing the spread of an infectious disease giving life-long immunity, in a community where individuals die and new individuals are born. The time to extinction of the disease starting in quasi-stationarity (conditional on non-extinction) is exponentially distributed. As the population size grows the epidemic process converges to a diffusion process. Properties of the limiting diffusion are used to obtain an approximate expression for tau, the mean-parameter in the exponential distribution of the time to extinction for the finite population. The expression is used to study how tau depends on the community size but also on certain properties of the disease/community: the basic reproduction number and the means and variances of the latency period, infectious period and life-length. Effects of introducing a vaccination program are also discussed as is the notion of the critical community size, defined as the size which distinguishes between the two qualitatively different behaviours.
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