Hi everybody

I have a controversy with someone about the world-3-03 as published in the Vensim documentation. When applying the extreme condition test, at a certain time, all people from cohort 0 to 14 years old die in a semester (the time step), the maturation goes negative, which means that people from cohort 15 to 44 are getting younger!.

Joined two published models in Vensim, with both results in two tables in the population view.

One with the original formulation and the other with the changed formulation.

To force mortality to 2, in a time step one uses the reality checks tool.

If one forces the mortality to 1, by setting the proportion of population 0 to 14 dying in the time step to 0.5, the number of people maturing goes to 0, which is still impossible, about half of the population from the beginning of the period maturing.

If one changes the formulation

( ( Population 0 To 14 ) )

* ( 1

- mortality 0 to 14 )

/ 15

To

( ( Population 0 To 14 ) )

* ( 1

- (mortality 0 to 14 * time step))

/ 15

The result resists the test.

The second formulation seems correct too because:

The population that matures in the time step is equal to the population at the beginning of the time step less the people that died during the time step divided by the number of time steps included in the duration of the cohort.

People maturing during the time step = (population - (population * mortality * time step)) / (15/time step) = maturation 14 to 15 * time step

Maturation 14 to 15 = People maturing during the time step / time step =

(population - (population * mortality * time step)) / 15 = population * (1 – (mortality * time step)) / 15.

The formula is too dimensionaly consistent.

People maturing during the time step (person)= (population (person) - (population * mortality * time step) (person)) / (15 (year) / time step (year)) = maturation 14 to 15 * time step

To make the formula

( ( Population 0 To 14 ) )

* ( 1

- mortality 0 to 14 )

/ 15

consistent one is obliged to affect a 1/year dimension to the 1 value and a no dimension to the 15.

For what reasons? 1 is in fact dimensionless and 15 is the duration of the cohort in years.

Both models can be read with either Vensim or the Vensim player.

Who is right?

Best regards.

Jean-Jacques Laublé