Modelling a population in terms of the number of individuals in different age-classes

ModelId:

ageclass6

SimileVersion:

5.9

This models a population of animals in terms of four age-classes. For each age-class, we use a compartment (state variable) to represent the number of individuals in that class. This version uses a four-instance submodel to represent the four age-classes. The ageing flow (from one class to the next) thus has to be handled by transferring the value for the outflow from each class to be assigned to the inflow for the next class.

Equations:

**Equations in Desktop**

births = sum([these_births])

pop size = sum([pop_size])

**Equations in Age class**

pop size: initial value = element([2,0,0,0],index(1))

ageing in = sum({ageing_next})

*Where: {ageing_next}=../Next class/ageing (to Age class in next)*

ageing out = element([1,0.2,0.1,0],index(1))*pop_size

births = if index(1)==1 then births else 0

deaths = m*pop_size

class = index(1)

m = element([0.05,0.01,0.01,0.05],index(1))

r = element([0,0.05,0.2,0.1],index(1))*(1-total_pop_size/100)

these births = r*pop_size

**Equations in Next class**

condition = class_next==class_this+1

*Where: class_this=../Age class/class (from Age class in this) class_next=../Age class/class (from Age class in next)*

ageing = ageing_out_this

*Where: ageing_out_this=../Age class/ageing out (from Age class in this)*

here: ageing_out_this=../Age class/ageing out (from Age class in this)/

Results:

ModelId:

ageclass5

SimileVersion:

5.9

This models a population of animals in terms of four age-classes. For each age-class, we use a compartment (state variable) to represent the number of individuals in that class.

Equations:

**Equations in Desktop**

births = sum([these_births])

pop size = sum([pop_size])

ageing = [ageing_out]

**Equations in Age class**

pop size: initial value = element([2,0,0,0],index(1))

births = if index(1) == 1 then births else 0

ageing out = element([1,0.2,0.1,0],index(1))*pop_size

deaths = m*pop_size

ageing in = if index(1)>1 then element([ageing],index(1)-1)else 0

m = element([0.05,0.01,0.01,0.05],index(1))

r = element([0,0.05,0.2,0.1],index(1))*(1-pop_size/100)

these births= r*pop_size

Results:

ModelId:

ageclass4

SimileVersion:

5.9

This models a population of animals in terms of four age-classes. For each age-class, we use a compartment (state variable) to represent the number of individuals in that class.

Equations:

Compartments

pop_size_1: initial value = 2

pop size_2: initial value = 0

pop size_3: initial value = 0

pop size_4: initial value = 0

Flows

ageing_1 = pop_size_1

ageing_2 = 0.2*pop_size_2

ageing_3 = 0.1*pop_size_3

births = births_2+births_3+births_4

deaths_1 = m1*pop_size_1

deaths_2 = m2*pop_size_2

deaths_3 = m3*pop_size_3

deaths_4 = m4*pop_size_4

Parameters

m1 = 0.05

m2 = 0.01

m3 = 0.01

m4 = 0.05

Intermediate variables

births_2 = r2*pop_size_2

births_3 = r3*pop_size_3

births_4 = r4*pop_size_4

pop size = pop_size_1+pop_size_2+pop_size_3+pop_size_4

r2 = 0.05*(1-pop_size/100)

r3 = 0.2*(1-pop_size/100)

Results: