Age-Structured Population Projection of Bangladesh by Using a Partial Differential Model with Quadratic Polynomial Curve Fitting

Affiliation(s)

^{1}
Department of Natural Sciences, Daffodil International University, Dhaka, Bangladesh.

^{2}
Department of Mathematics, Jahangirnagar University, Dhaka, Bangladesh.

ABSTRACT

In this paper, the age-specific population of Bangladesh based on a linear first order (hyperbolic) partial differential equation which is known as Von-Foerster Equation is studied. Applying quadratic polynomial curve fitting, the total population and population density of Bangladesh are projected for the years 2001 to 2050 based on the explicit upwind finite difference scheme for the age-structured population model based on given data (source: BBS & ICDDR, B) for initial value in the year 2001. For each age-group, the future birth rates and death rates are estimated by using quadratic polynomial curve fitting of the data for the years 2001 to 2012. Quadratic polynomial curve fitting is also used for the boundary value as the (0 - 4) age-group population based on the population size of the age-group for the years 2001 to 2012.

In this paper, the age-specific population of Bangladesh based on a linear first order (hyperbolic) partial differential equation which is known as Von-Foerster Equation is studied. Applying quadratic polynomial curve fitting, the total population and population density of Bangladesh are projected for the years 2001 to 2050 based on the explicit upwind finite difference scheme for the age-structured population model based on given data (source: BBS & ICDDR, B) for initial value in the year 2001. For each age-group, the future birth rates and death rates are estimated by using quadratic polynomial curve fitting of the data for the years 2001 to 2012. Quadratic polynomial curve fitting is also used for the boundary value as the (0 - 4) age-group population based on the population size of the age-group for the years 2001 to 2012.

Cite this paper

Sultana, S. , Hasan, M. and Andallah, L. (2015) Age-Structured Population Projection of Bangladesh by Using a Partial Differential Model with Quadratic Polynomial Curve Fitting.*Open Journal of Applied Sciences*, **5**, 542-551. doi: 10.4236/ojapps.2015.59052.

Sultana, S. , Hasan, M. and Andallah, L. (2015) Age-Structured Population Projection of Bangladesh by Using a Partial Differential Model with Quadratic Polynomial Curve Fitting.

References

[1] Murray, J.D. (1989) Mathematical Biology. Springer-Verlag, Berlin Hiedelberg.

[2] Webb, G.F. (1985) Theory of Nonlinear Age-Dependent Population Dynamics. Marcel Dekker Inc., New York.

[3] Gurtin, M.E. and MacCamy, R.C. (1984) Nonlinear Age-Dependent Population Dynamics. Archive for Rational Mechanics and Analysis, 54, 281-300.

[4] Iannelli, M. (1995) Mathematical Theory of Age-Structured Population Dynamics. Applied Mathematics Monographs, 7, Consiglio Nazionaledelle Ricerche, Pisa.

[5] Burden, R.I. and Fairs, J.D. (1997) Numerical Analysis. 6th Edition, Brookscole.

[6] Abia, L.M., Angulo, O. and Lopez-Marcos, J.C. (2005) Age-Structured Population Models and Their Numerical Solution. Ecological Modelling, 188, 112-136.

http://dx.doi.org/10.1016/j.ecolmodel.2005.05.007

[7] ICDDR, B Document, Table 2.3 Mid-Year Population Distribution by Age Group.

[8] ICDDR, B Document, Table 3.3 Death Rate by Age and Year (per 1000 Population).

[9] Kabir, Md. and Ahmed, T. (2006) Poverty-Aging Population Projection. BBS, Ministry of planning, Bangladesh.

[10] Dutta and Andallah, L.S. (2008) Age-Structured Population Projection in Bangladesh Based on Numerical Solution of a Deterministic Model. Bangladesh Journal of Scientific Research, 21, 65-78.

[11] Haque, Md.M., Ahmed, F., Anam, S. and Kabir, Md.R. (2012) Future Population Projection of Bangladesh by Growth Rate Modeling Using Logistic Population Model. Annals of Pure and Applied Mathematics, 1, 192-202.

[1] Murray, J.D. (1989) Mathematical Biology. Springer-Verlag, Berlin Hiedelberg.

[2] Webb, G.F. (1985) Theory of Nonlinear Age-Dependent Population Dynamics. Marcel Dekker Inc., New York.

[3] Gurtin, M.E. and MacCamy, R.C. (1984) Nonlinear Age-Dependent Population Dynamics. Archive for Rational Mechanics and Analysis, 54, 281-300.

[4] Iannelli, M. (1995) Mathematical Theory of Age-Structured Population Dynamics. Applied Mathematics Monographs, 7, Consiglio Nazionaledelle Ricerche, Pisa.

[5] Burden, R.I. and Fairs, J.D. (1997) Numerical Analysis. 6th Edition, Brookscole.

[6] Abia, L.M., Angulo, O. and Lopez-Marcos, J.C. (2005) Age-Structured Population Models and Their Numerical Solution. Ecological Modelling, 188, 112-136.

http://dx.doi.org/10.1016/j.ecolmodel.2005.05.007

[7] ICDDR, B Document, Table 2.3 Mid-Year Population Distribution by Age Group.

[8] ICDDR, B Document, Table 3.3 Death Rate by Age and Year (per 1000 Population).

[9] Kabir, Md. and Ahmed, T. (2006) Poverty-Aging Population Projection. BBS, Ministry of planning, Bangladesh.

[10] Dutta and Andallah, L.S. (2008) Age-Structured Population Projection in Bangladesh Based on Numerical Solution of a Deterministic Model. Bangladesh Journal of Scientific Research, 21, 65-78.

[11] Haque, Md.M., Ahmed, F., Anam, S. and Kabir, Md.R. (2012) Future Population Projection of Bangladesh by Growth Rate Modeling Using Logistic Population Model. Annals of Pure and Applied Mathematics, 1, 192-202.