POPULATION FORECASTING LOGISTIC CURVE METHOD Page 1 GROUP

POPULATION FORECASTING LOGISTIC CURVE METHOD Page 1

GROUP MEMBERS Kush Poorunsing Aman Sahadeo Arshaad Jeedaran Nevin Sunassee Pamben Moonsamy Kishan Joorawon Page 2

Population Forecasting • Important process in the design of waste water treatment plants • Factors affecting change in population: § Fertility/ Birth rate § Death rate § Migration Page 3

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. Population Decreasing rate Increasing rate Low rate Years Page 4

Equation - 1 • Page 5

Equation - 2 • Page 6

Equation - 3 • Page 7

Example Census year Population 1851 495 1861 693 1901 3162 1911 4829 1921 6584 1931 8202 1944 11885 1952 13333 1962 18335 1972 24769 1983 33082 1990 34204 2000 35779 • The data for population censuses from 1851 to 2000 for 1871 1108 Island of Rodrigues is given below. Estimate the 1881 1431 expected population in 2011. 1891 2068 Page 8

STEP 1 Census year Population 1851 495 1861 693 1871 1108 1921 6584 1931 8202 1944 11885 1952 13333 1962 18335 1972 24769 1983 33082 1990 34204 2000 35779 1881 1431 • Three successive years, represented by t o, 1891 2068 t 1, and t 2 are chosen such that they are 1901 3162 equidistant from each other. 1911 4829 t 0 t 1 t 2 Page 9

Logistic Curve Plot 40000 35000 30000 Population 25000 20000 15000 10000 5000 0 1831 1851 1871 1891 1911 1931 Census year 1951 1971 1991 2011 Page 10

STEP 2 Census year Population 1851 495 1861 693 1871 1108 1911 4829 1921 6584 1931 8202 1944 11885 1952 13333 1962 18335 1972 24769 1983 33082 1990 34204 2000 35779 1881 1431 to t and t to • The number of years from t o 1 1 1891 2068 t 2 is denoted by n. 1901 3162 t 0 n=28 t 1 n=28 t 2 Page 11

STEP 3 Census year Population 1851 495 1861 693 1871 1108 1921 6584 1931 8202 1944 11885 1952 13333 1962 18335 1972 24769 1983 33082 1990 34204 2000 35779 1881 1431 • The population figures corresponding to t o, 1891 2068 t 1, and t 2 are P , P and P respectively o 1 2 1901 3162 through which the logistic curve is to pass. 1911 4829 t 0 n=28 t 1 n=28 t 2 P 0 P 1 P 2 Page 12

CALCULATIONS - 1 • Page 13

CALCULATIONS - 2 • Page 14

CALCULATIONS - 3 • Page 15

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 16

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 17

References • Punmia, B. C, Arun, K. J. , 2005. Water Supply Engineering. 2 nd ed. New Delhi: Laxmi Publications • Annual Digest of Statistics 2011 [Online]. Available from: http: //www. gov. mu/portal/goc/cso/file/Annual. Dig estof. Statistics 2011. pdf • Rodrigues [Online]. Available from: http: //en. wikipedia. org/wiki/Rodrigues Page 18

Thank You For Your Attention Page 19