# Generation Time

Generation time is a quantity used in population biology and demography to reflect the relative size of intervals of offspring production. Generation time usually expresses the average age of breeding females within a population. In epidemiology, it is defined as the interval of time between receipt of infection by a host and maximal infectivity of that host. Suppose females begin breeding at age and stop breeding (or die) at age, then the average age of first reproduction of a cohort of females is

$T = \frac{\sum_{x=\alpha}^{\omega} x l(x) m(x) }{\sum_{x=\alpha}^{\omega} l(x) m(x) }$

where is the hazard function and is the fecundity of females aged .

When the population is in stable age distribution, we can express the generation time as the average age of mothers of zero-year-olds:

$T = \sum_{x=\alpha}^{\omega} x e^{-rx} l(x) m(x)$

where is the Malthusian parameter of the population.

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They shall beget and rear children, handing on the torch of life from one generation to another.
Plato (c. 427–347 B.C.)

last time I saw you was the hospital
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the war in Spain has ended long ago
Aunt Rose
Allen Ginsberg (b. 1926)