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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 - PowerPoint PPT Presentation
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Page 1
POPULATION FORECASTING -
LOGISTICCURVE
METHOD
Page 2
GROUP MEMBERS
Kush PoorunsingAman Sahadeo
Arshaad JeedaranNevin Sunassee
Pamben MoonsamyKishan Joorawon
Page 3
Population Forecasting
• Important process in the design of waste water treatment plants
• Factors affecting change in population: Fertility/ Birth rate Death rate Migration
Page 4
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
Page 5
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
Page 6
Equation - 2
• ……………….. (2)• WherePsat: population at saturation level Po: base population P1 , P2 : population at time periods
Page 7
Equation - 3
• …………………. (3)
• ………………(4)• Wheren: time interval between successive censuses
Page 8
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.
Page 9
Census year Population
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
Page 10
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
Page 11
Census year Population
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
Page 12
Census year Population
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
Page 13
CALCULATIONS - 1
• n=28• P0= 11885, P1= 24769 and P2= 35779• From equation 2,
• ∴
Page 14
CALCULATIONS - 2
• From equation 3, • ∴
• From equation 4, • ∴
Page 15
CALCULATIONS - 3
• Replacing the values obtained in equation 1, the expected population for 2011 is:
• = 2011-1944 = 67 years•
Page 16
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
Page 17
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
Page 18
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
Page 19
Thank You For Your Attention