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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

POPULATION FORECASTING - Logistic

CURVE

METHOD


Group members

GROUP MEMBERS

Kush Poorunsing

AmanSahadeo

ArshaadJeedaran

NevinSunassee

PambenMoonsamy

KishanJoorawon


Population forecasting

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

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

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

Equation - 2

  • ……………….. (2)

  • Where

    Psat: population at saturation level

    Po: base population

    P1, P2: population at time periods


Equation 3

Equation - 3

  • …………………. (3)

  • ………………(4)

  • Where

    n: time interval between successive censuses


Example

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

STEP 1

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

t0

t1

t2


Logistic curve plot

Logistic Curve Plot


Step 2

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

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

CALCULATIONS - 1

  • n=28

  • P0= 11885, P1= 24769 and P2= 35779

  • From equation 2,


Calculations 2

CALCULATIONS - 2

  • From equation 3,

  • From equation 4,


Calculations 3

CALCULATIONS - 3

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

  • = 2011-1944 = 67 years


Conclusion

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 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

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


Population forecasting logistic curve method

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