POPULATION FORECASTING - Logistic CURVE METHOD

POPULATION FORECASTING -

LOGISTICCURVE

METHOD

GROUP MEMBERS

Kush PoorunsingAman Sahadeo

Arshaad JeedaranNevin Sunassee

Pamben MoonsamyKishan Joorawon

Population Forecasting

• Important process in the design of waste water treatment plants

• Factors affecting change in population: Fertility/ Birth rate Death rate Migration

Logistic Method

• Follows some logical mathematical relationship.

• has an S-shape combining a geometric rate of growth at low population with a declining growth rate as the population approaches some limiting value.

Years

Popu

latio

n

Low rate

Increasing rate

Decreasing rate

Saturation population

Equation - 1

• ………………. (1)• WherePt : population at some time in the future Psat: population at saturation level t: number of years after base year a, b: data constants

Equation - 2

• ……………….. (2)• WherePsat: population at saturation level Po: base population P1 , P2 : population at time periods

Equation - 3

• …………………. (3)

• ………………(4)• Wheren: time interval between successive censuses

Census year Population

1851 4951861 6931871 11081881 14311891 20681901 31621911 48291921 65841931 82021944 118851952 133331962 183351972 247691983 330821990 342042000 35779

Example• The data for population censuses from 1851 to 2000 for

Island of Rodrigues is given below. Estimate the expected population in 2011.


1851 4951861 6931871 11081881 14311891 20681901 31621911 48291921 65841931 82021944 118851952 133331962 183351972 247691983 330821990 342042000 35779

STEP 1

• Three successive years, represented by to, t1, and t2 are chosen such that they are equidistant from each other.

t0

t1

t2

Logistic Curve Plot

1840 1860 1880 1900 1920 1940 1960 1980 2000 20200

5000

10000

15000

20000

25000

30000

35000

40000

Census year

Popu

latio

n


1851 4951861 6931871 11081881 14311891 20681901 31621911 48291921 65841931 82021944 118851952 133331962 183351972 247691983 330821990 342042000 35779

STEP 2

• The number of years from to to t1 and t1 to t2 is denoted by n.

n=28

n=28

t0

t1

t2


1851 4951861 6931871 11081881 14311891 20681901 31621911 48291921 65841931 82021944 118851952 133331962 183351972 247691983 330821990 342042000 35779

STEP 3

• The population figures corresponding to to, t1, and t2 are Po, P1 and P2 respectively through which the logistic curve is to pass.

P0

P1

P2

n=28

n=28

t0

t1

t2

CALCULATIONS - 1

• n=28• P0= 11885, P1= 24769 and P2= 35779• From equation 2,

• ∴

CALCULATIONS - 2

• From equation 3, • ∴

• From equation 4, • ∴

CALCULATIONS - 3

• Replacing the values obtained in equation 1, the expected population for 2011 is:

• = 2011-1944 = 67 years•

CONCLUSION

• Based on census reports, the population of Rodrigues in 2011 was 37,922 (Wikipedia)

• Estimated population with logistic method is 38420.8

• 1.31% deviation from actual value

Advantages and Disadvantages

• Advantages Longer projection period compared to simple geometric

procedures Gives a better approximation than other methods.

• Disadvantages Mechanical process Cannot predict decreasing population Demographic and socioeconomic changes not considered Requires a large number of observations covering a long

period

References• Punmia, B.C, Arun, K.J., 2005. Water Supply

Engineering. 2nd ed. New Delhi: Laxmi Publications

• Annual Digest of Statistics 2011 [Online]. Available from: http://www.gov.mu/portal/goc/cso/file/AnnualDigestofStatistics2011.pdf

• Rodrigues [Online]. Available from: http://en.wikipedia.org/wiki/Rodrigues

Thank You For Your Attention

POPULATION FORECASTING - Logistic CURVE METHOD

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