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POPULATION FORECASTING - Logistic CURVE METHODPowerPoint Presentation

POPULATION FORECASTING - Logistic CURVE METHOD

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GROUP MEMBERS

Kush Poorunsing

AmanSahadeo

ArshaadJeedaran

NevinSunassee

PambenMoonsamy

KishanJoorawon

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

Saturation population

- 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.

Equation - 1

- ………………. (1)
- Where
Pt: 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)
- Where
Psat: population at saturation level

Po: base population

P1, P2: population at time periods

Equation - 3

- …………………. (3)
- ………………(4)
- Where
n: time interval between successive censuses

Example

- The data for population censuses from 1851 to 2000 for Island of Rodrigues is given below. Estimate the expected population in 2011.

STEP 1

- Three successive years, represented by to, t1, and t2are chosen such that they are equidistant from each other.

t0

t1

t2

STEP 3

- The population figures corresponding to to, t1, and t2are Po, P1and P2respectivelythrough which the logistic curve is to pass.

t0

P0

n=28

t1

P1

n=28

P2

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

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