Modelling population dynamics using age-structured system of partial differential equations

  • Authors

    • Zachariah Kemei University of Eldoret, Department of Mathematics and Computing. P.O. Box 125 - 30100, Eldoret – Kenya
    • Titus Rotich Moi University P.O. BOX 3900 - 30100 ELDORET - KENYA
    • Jacob Bitok University of Eldoret, Department of Mathematics and Computing. P.O. Box 125 - 30100, Eldoret – Kenya
    2024-10-31
    https://doi.org/10.14419/m81azj37
  • Age-Structured; Constrictive; Dependency Ratio; Expansive; Population; Simulation

  • Abstract

    In this paper, an age-structured model was used to model population dynamics, and make predictions through simulation using 2019 Kenya population data. The age-structured mathematical model was developed, using partial differential equations on population densities as func-tions of age and time. The population was structured into 20 clusters each of 5 year interval, and assigned different birth and death rate pa-rameters. Crank-Nicolson numerical scheme was used to simulate the model and the 2019 initial population of 38,589,011 was found to increase by 50% to 57,956,100 by 2050. The initial economic dependency ratio was computed to be 1:2, but due to changes in technology and improvement of living standards, the new ratio is lowered to 1:1.14. The graphical presentation showed a trend of transition from ex-pansive to constrictive population pyramid.

     

    Author Biography

    • Titus Rotich, Moi University P.O. BOX 3900 - 30100 ELDORET - KENYA

      Head of Subject

      Mathematics Department

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  • How to Cite

    Kemei , Z. ., Rotich, T. ., & Bitok , J. . (2024). Modelling population dynamics using age-structured system of partial differential equations. International Journal of Applied Mathematical Research, 13(2), 110-116. https://doi.org/10.14419/m81azj37