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POPULATION FORECASTING - Logistic CURVE METHOD. GROUP MEMBERS. Kush Poorunsing Aman Sahadeo Arshaad Jeedaran Nevin Sunassee Pamben Moonsamy Kishan Joorawon. Population Forecasting. Important process in the design of waste water treatment plants

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POPULATION FORECASTING - Logistic CURVE METHOD

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POPULATION FORECASTING - Logistic

CURVE

METHOD

Kush Poorunsing

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 2

• The number of years from toto t1and t1 to t2 is denoted by n.

t0

n=28

t1

n=28

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

• Longer projection period compared to simple geometric procedures

• Gives a better approximation than other methods.

• 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