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Pa+1,s,t+1=Pa,s,t⋅Sa,s,t+Ma,s,tP_{a+1,s,t+1} = P_{a,s,t} \cdot S_{a,s,t} + M_{a,s,t}

Why this formula appears here

Aging the cohort forward. For each one-year (or five-year) step, every age-sex cohort is advanced by applying an age-specific survival ratio — the probability of surviving from one age to the next, derived from a life table built out of registered deaths and mortality schedules — and then subtracting deaths and adding net migrants assigned to that same age and sex [ 1 ] . Symbolically, for a cohort of age a and sex s in year t : Pa+1,s,t+1=Pa,s,t⋅Sa,s,t+Ma,s,tP_{a+1,s,t+1} = P_{a,s,t} \cdot S_{a,s,t} + M_{a,s,t}. where P is the population count, S is the age-and-sex-specific survival ratio for that interval, and M is net migration assigned to that cohort during the interval. The youngest cohort in each step is not aged forward from an existing cohort; it…

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Pa+1,s,t+1P_{a+1,s,t+1}

Symbol P_a+1,s,t+1

PaP_a+1,s,t+1 is part of the quantity the equation computes from the expression on the right.

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Pa,s,tP_{a,s,t}

Symbol P_a,s,t

PaP_a,s,t is one of the signed contributions combined to compute the quantity on the left.

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Sa,s,tS_{a,s,t}

Symbol S_a,s,t

SaS_a,s,t is one of the signed contributions combined to compute the quantity on the left.

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Ma,s,tM_{a,s,t}

Symbol M_a,s,t

MaM_a,s,t is one of the signed contributions combined to compute the quantity on the left.

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Published contexts (1)

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Pa+1,s,t+1=Pa,s,t⋅Sa,s,t+Ma,s,tP_{a+1,s,t+1} = P_{a,s,t} \cdot S_{a,s,t} + M_{a,s,t}

Equation 4 · Human Systems

Demography, Migration, and Urban Futures in Practice: An Advanced Technical Guide

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Aging the cohort forward. For each one-year (or five-year) step, every age-sex cohort is advanced by applying an age-specific survival ratio — the probability of surviving from one age to the next, derived from a life table built out of registered deaths and mortality schedules — and then subtracting deaths and adding net migrants assigned to that same age and sex [ 1 ] . Symbolically, for a cohort of age a and sex s in year t : Pa+1,s,t+1=Pa,s,t⋅Sa,s,t+Ma,s,tP_{a+1,s,t+1} = P_{a,s,t} \cdot S_{a,s,t} + M_{a,s,t}. where P is the population count, S is the age-and-sex-specific survival ratio for that interval, and M is net migration assigned to that cohort during the interval. The youngest cohort in each step is not aged forward from an existing cohort; it…

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