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In epidemiology, the basic reproduction number (sometimes called basic reproductive ratio, or incorrectly basic reproductive rate, and denoted ''R''0, ''r naught'') of an infection can be thought of as the number of cases one case generates on average over the course of its infectious period, in an otherwise uninfected population.〔Free text〕 This metric is useful because it helps determine whether or not an infectious disease can spread through a population. The roots of the basic reproduction concept can be traced through the work of Alfred Lotka, Ronald Ross, and others, but its first modern application in epidemiology was by George MacDonald in 1952, who constructed population models of the spread of malaria. When :''R''0 < 1 the infection will die out in the long run. But if :''R''0 > 1 the infection will be able to spread in a population. Generally, the larger the value of ''R''0, the harder it is to control the epidemic. For simple models and a 100%-effective vaccine, the proportion of the population that needs to be vaccinated to prevent sustained spread of the infection is given by 1 − 1/''R''0. The basic reproduction number is affected by several factors including the duration of infectivity of affected patients, the infectiousness of the organism, and the number of susceptible people in the population that the affected patients are in contact with. In populations that are not homogeneous, the definition of ''R''0 is more subtle. The definition must account for the fact that a typical infected individual may not be an average individual. As an extreme example, consider a population in which a small portion of the individuals mix fully with one another while the remaining individuals are all isolated. A disease may be able to spread in the fully mixed portion even though a randomly selected individual would lead to fewer than one secondary case. This is because the typical infected individual is in the fully mixed portion and thus is able to successfully cause infections. In general, if the individuals who become infected early in an epidemic may be more (or less) likely to transmit than a randomly chosen individual late in the epidemic, then our computation of ''R''0 must account for this tendency. An appropriate definition for ''R''0 in this case is "the expected number of secondary cases produced by a typical infected individual early in an epidemic". ==Other uses== ''R''0 is also used as a measure of individual reproductive success in population ecology, evolutionary invasion analysis and life history theory. It represents the average number of offspring produced over the lifetime of an individual (under ideal conditions). For simple population models, ''R''0 can be calculated, provided an explicit decay rate (or "death rate") is given. In this case, the reciprocal of the decay rate (usually 1/''d'') gives the average lifetime of an individual. When multiplied by the average number of offspring per individual per timestep (the "birth rate" ''b''), this gives ''R''0 = ''b'' / ''d''. For more complicated models that have variable growth rates (e.g. because of self-limitation or dependence on food densities), the maximum growth rate should be used. 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「basic reproduction number」の詳細全文を読む スポンサード リンク
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