# MATHEMATICAL APPROACH ON HOUSEHOLD WASTE CAUSING ENVIRONMENTAL POLLUTANTS DUE TO LANDFILL AND TREATMENTS

• Nita H. Shah Department of Mathematics, Gujarat University, Ahmedabad, 380009, Gujarat, India
• Moksha H. Satia Department of Mathematics, Gujarat University, Ahmedabad, 380009, Gujarat, India
• Foram A. Thakkar Department of Mathematics, Gujarat University, Ahmedabad, 380009, Gujarat, India
Keywords: Household Solid Waste, System of Non-Linear Differential Equations, Basic Reproduction Number, Local Stability, Global Stability, Environmental Pollutants

### Abstract

Household solid waste is the solid waste mixture of garbage and rubbish which comes during the use of various products in daily life. It also called as domestic waste or residential waste. It may fall into two categories either hazardous or non-hazardous which are stored and forsaken directly to the landfills. This is how household solid waste plays vital role in spreading environmental pollutants. For reduction of the pollution, treatment plant is constructed for hazardous solid waste and compost plant is organized for non-hazardous solid waste. In this paper, we have developed a system of non-linear differential equations to analyse the household solid waste storage. In order of preventive measures, five various controls are given to the different compartments. The basic reproduction number and the stability are derived to check the endurance of the model. The numerical simulation is also done using validated data.

### References

Benítez, Sara Ojeda, et al. "Mathematical modeling to predict residential solid waste generation." Waste Management 28 (2008): S7-S13. DOI: https://doi.org/10.1016/j.wasman.2008.03.020

Choe, Chongwoo, and Iain Fraser. "An economic analysis of household waste management." Journal of environmental economics and management 38.2 (1999): 234-246. DOI: https://doi.org/10.1006/jeem.1998.1079

Dyson, Brian, and Ni-Bin Chang. "Forecasting municipal solid waste generation in a fast-growing urban region with system dynamics modeling." Waste management 25.7 (2005): 669-679. DOI: https://doi.org/10.1016/j.wasman.2004.10.005

Fleming, W. H., &Rishel, R. W. (2012). Deterministic and stochastic optimal control (Vol. 1). Springer Science & Business Media.

La Salle, Joseph P. The stability of dynamical systems. Society for Industrial and Applied Mathematics, 1976. DOI: https://doi.org/10.1137/1.9781611970432

Moberg, Åsa, et al. "Life cycle assessment of energy from solid waste—part 2: landfilling compared to other treatment methods." Journal of Cleaner Production 13.3 (2005): 231-240. DOI: https://doi.org/10.1016/j.jclepro.2004.02.025

Pontriagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., Mishchenko, E. F., (1986)."The Mathematical Theory of Optimal Process", Gordon and Breach Science Publishers, NY, USA, 4- 5.

Routh, E. J. (1877). A treatise on the stability of a given state of motion: particularly steady motion. Macmillan and Company.

Shah, Nita H., H. Satia, and M. Yeolekar. "Optimal Control on depletion of Green Belt due to Industries." Advances in Dynamical Systems and Applications 12.3 (2017): 217-232.

Shah, Nita H., Moksha H. Satia, and Bijal M. Yeolekar. "Optimum Control for Spread of Pollutants through Forest Resources." Applied Mathematics 8.05 (2017): 607. DOI: https://doi.org/10.4236/am.2017.85047

UdayaSimha, L., and K. N. Achyuth. "MATHEMATICAL MODELING OF HOUSEHOLD WASTEWATER TREATMENT BY DUCKWEED BATCH REACTOR."

Published
2018-02-28
How to Cite
Shah, N., Satia, M., & Thakkar, F. (2018). MATHEMATICAL APPROACH ON HOUSEHOLD WASTE CAUSING ENVIRONMENTAL POLLUTANTS DUE TO LANDFILL AND TREATMENTS . International Journal of Engineering Technologies and Management Research, 5(2), 266-282. https://doi.org/10.29121/ijetmr.v5.i2.2018.171
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Articles