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A model for the effect of density of human population on the depletion of dissolved oxygen in a water body

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  • A. Misra
  • P. Tiwari

Abstract

A nonlinear mathematical model to study the effect of density of human population on the depletion of dissolved oxygen in a water body is proposed and analyzed. The proposed model is governed by interactions among five dependent variables, namely density of resource biomass, density of human population, concentration of organic pollutants, density of bacteria and concentration of dissolved oxygen. In the model formulation, it is assumed that density of resource biomass and density of human population follow logistic models with prey--predator type interaction. The model is analyzed using stability theory of differential equations. The analysis of model shows that increase in human population intensify the depletion in concentration of dissolved oxygen in a water body. Numerical simulations are carried out to illustrate analytical findings. Copyright Springer Science+Business Media Dordrecht 2015

Suggested Citation

  • A. Misra & P. Tiwari, 2015. "A model for the effect of density of human population on the depletion of dissolved oxygen in a water body," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 17(3), pages 623-640, June.
    • Handle: RePEc:spr:endesu:v:17:y:2015:i:3:p:623-640
    DOI: 10.1007/s10668-014-9565-2
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    References listed on IDEAS

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    1. A. Misra & Kusum Lata & J. Shukla, 2014. "Effects of population and population pressure on forest resources and their conservation: a modeling study," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 16(2), pages 361-374, April.
    2. M. Sudha & S. Ravichandran & R. Sakthivadivel, 2013. "Water Bodies Protection Index for assessing the sustainability status of lakes under the influence of urbanization: a case study of south Chennai, India," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 15(5), pages 1157-1171, October.
    3. Amemiya, Takashi & Enomoto, Takatoshi & Rossberg, Axel G. & Yamamoto, Tetsuya & Inamori, Yuhei & Itoh, Kiminori, 2007. "Stability and dynamical behavior in a lake-model and implications for regime shifts in real lakes," Ecological Modelling, Elsevier, vol. 206(1), pages 54-62.
    4. K. Parameswari & B. Mudgal & Prakash Nelliyat, 2012. "Evaluation of groundwater contamination and its impact: an interdisciplinary approach," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 14(5), pages 725-744, October.
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    Cited by:

    1. Abhinav Tandon & Kumari Jyotsna & Susanto Dey, 2018. "A mathematical model to investigate the impact of overgrowing population-induced mining on forest resources," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 20(4), pages 1499-1516, August.

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