| 来源类型 | Article
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| 规范类型 | 其他
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| DOI | 10.1007/s00285-012-0575-0
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| Necessary and sufficient conditions for R0 to be a sum of contributions of fertility loops. |
| Rueffler C; Metz JAJ
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| 发表日期 | 2013
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| 出处 | Journal of Mathematical Biology 66 (4): 1099-1122
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| 出版年 | 2013
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| 语种 | 英语
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| 摘要 | Recently, de-Camino-Beck and Lewis (Bull Math Biol 69:1341.1354, 2007) have presented a method that under certain restricted conditions allows computing the basic reproduction ratio R0 in a simple manner from life cycle graphs, without, however, giving an explicit indication of these conditions. In this paper, we give various sets of sufficient and generically necessary conditions. To this end, we develop a fully algebraic counterpart of their graph-reduction method which we actually found more useful in concrete applications. Both methods, if they work, give a simple algebraic formula that can be interpreted as the sum of contributions of all fertility loops. This formula can be used in e.g. pest control and conservation biology, where it can complement sensitivity and elasticity analyses. The simplest of the necessary and sufficient conditions is that, for irreducible projection matrices, all paths from birth to reproduction have to pass through a common state. This state may be visible in the state representation for the chosen sampling time, but the passing may also occur in between sampling times, like a seed stage in the case of sampling just before flowering. Note that there may be more than one birth state, like when plants in their first year can already have different sizes at the sampling time. Also the common state may occur only later in life. However, in all cases R0 allows a simple interpretation as the expected number of new individuals that in the next generation enter the common state deriving from a single individual in this state. We end with pointing to some alternative algebraically simple quantities with properties similar to those of R0 that may sometimes be used to good effect in cases where no simple formula for R0 exists. |
| 主题 | Evolution and Ecology (EEP)
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| 关键词 | Basic reproduction ratio
Conservation
Invasion
Matrix models
Population persistence
R0
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| URL | http://pure.iiasa.ac.at/id/eprint/10511/
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| 来源智库 | International Institute for Applied Systems Analysis (Austria)
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| 引用统计 |
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| 资源类型 | 智库出版物
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| 条目标识符 | http://119.78.100.153/handle/2XGU8XDN/129818
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推荐引用方式
GB/T 7714 |
Rueffler C,Metz JAJ. Necessary and sufficient conditions for R0 to be a sum of contributions of fertility loops.. 2013.
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