Mathematical Modelling of Deforestation of Forested Area Due to Lack of Awareness of Human Population and Its Conservation
Mathematical Modelling and Applications
Volume 5, Issue 2, June 2020, Pages: 94-104
Received: Jan. 3, 2020; Accepted: Mar. 10, 2020; Published: May 12, 2020
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Ararso Hussen Teru, Department of Mathematics, Wolkite University, Wolkite, Ethiopia
Purnachandra Rao Koya, Department of Mathematics, Wollega University, Nekemte, Ethiopia
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As the density of human population increases the forest density will be highly affected by population from time to time for agricultural, industrial, economic purpose, and etc. Because of lack of awareness about the importance of forestry resources, the human populations clear forests for different purposes. Keeping this in mind, a nonlinear mathematical model is proposed and analyzed to study the deforestation of forest resources due to lack of clear information about utility of the forest as well as to increase forestry resources by plantation on the conservation of forestry resources. The model is in the form of ordinary differential equations. The result of this study shows that as the density of population as well as population pressure increases, the cumulative density of forest resources decreases. Reversely, the test of supporting human awareness on the importance of forest resources for global purposes show that as awareness of human population increases the declaration of forest resources decreases. In addition to this, increasing the density of forest resources through plantation may replace the clear-cut of forest area. This help the conservation carried out to in force the pressure of human population to save the forest density and forest habit. For these findings analytical and numerical analyses are performed.
Mathematical Model, Logistic Growth Model, Forest Density, Population Density, Population Pressure, Numerical Simulation
To cite this article
Ararso Hussen Teru, Purnachandra Rao Koya, Mathematical Modelling of Deforestation of Forested Area Due to Lack of Awareness of Human Population and Its Conservation, Mathematical Modelling and Applications. Vol. 5, No. 2, 2020, pp. 94-104. doi: 10.11648/
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This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A. K. Misra and Kusum Lata, A mathematical model to achieve sustainable forest management Vol. 6, No. 4 (2015) 1550040 (18 pages).
A. K. Misra, Kusum Lata, Depletion and Conservation of Forestry Resources: A Mathematical Model, January (2015) 23 (1): 25-41.
A. K. Misra, Kusum Lata and J. B. Shukla, Effects of population and population pressureon forest resources and their conservation: a modeling study, (2014) 16: 361-374.
Misra, AK and Lata, Kusum and Shukla, JBA mathematical model for the depletion offorestry resources due to population and population pressure augmented industrialization, vol. 5, n. 01, p. 1350022, (2014).
Shukla, JB and Lata, Kusum and Misra, AK (2011), modeling the depletion of a renewable resource by population and industrialization: Effect of technology on its conservation.
Abdurahiman Kubsa, Granting exclusive user rights to the forest dwellers in the state owned forest: the WAJIB approach in Ethiopia.
AbrahaHatsey, Tend of forest cover change in ethiopia; Paper presented in South AfricaGeorg-August University Gottingen, September, 2015.
Math 4330, Numerical Solution of ODEs Using Matlab.
Andam, Emmanuel Appoh, Analysis of transmission of dynamics Tuberculosis (TB) usingdifferential equations: A case study of Amansie west district, Ghana, 2013.
ArarsaRegassa, DidhaDiriba, GedefaNegera, Bale Mountains Eco-region Reduction ofEmission from Deforestation and Forest Degradation (REDD+) Project Ethiopia.
Atasi Patra (2013), Dynamics of Biological Species: Some Mathematical Models, December, 2013.
B. Dubey, S. Sharma, P. Sinha and J. B. Shukla, Modelling the depletion of forestry resources by population and population pressure augmented industrialization, AppliedMathematical Modelling 33 2009, 3002-3014.
FekaduGurmessa, Forest loss and climate change in Ethiopia, Vol. 4 (5), pp. 216-224, May. 2015.
GirmaAmente. Integrated and participatory forest management in the Bale Mountainsof Ethiopia, 2006.
LudekBerec. Mathematical modeling in ecology and epidemiology July 2011.
Manju Agarwal, RachanaPathak, Conservation of Forestry Biomass with the Use of Alternative Resource, Open Journal of Ecology, 2015, 5, 87-109.
Manju Agarwal, Tazeen Fatima and H. I. Freedman, Depletion of forestry resourcebiomass due to industrialization pressure: a ratio-dependent mathematical model, Journal of Biological Dynamics, 2010 4: 4 381-396.
Mette LoycheWilkie, VialedelleTerme di Caracalla Global forest resources assessment2010 country report EthiopaFAO Forestry Department Rome 00153, Italy (2010).
MulugetaLemenih and HabtemariamKassa, Re-Greening Ethiopia: History, Challenges and Lessons Forests 2014, 5, 1896-1909; doi: 10.3390/f5081896.
Nadhurah BT Abdul Halim, Tuberculosis Model: A mathematical analysis, 2015.
Netsanet Deneke, Land use and Land Cover changes in Harenna Forest and Surrounding area, Bale Mountain national park, 2007.
Robert Repet to and Thomas Holmes, The Role of Population in Resource Depletion inDeveloping Countries, Vol. 9, No. 4 (Dec., 1983), pp. 609-632.
Shyam Sundar, Effect of Elevated Carbon Dioxide Concentration on Plant Growth: A Mathematical Model, American Journal of Applied Mathematics and Statistics, 2015, Vol. 3, No. 2, 59-67.
Sisay Nune Hailemariam, Teshome Soromessa and Demel Teketay, Non-carbon benefits for effective implementation of REDD+: The case of Bale Mountains Eco-Region, Southeastern Ethiopia, 2015.
Shukla J. B., Freedman, H. I., Pal, V. N., Misra, O. P., Agarwal, M. and Shukla, A., Degradation and subsequent regeneration of a forestry resource: a mathematical model, Ecol. Model., 44, 219-229, 1989.
TerefeDegeti, Factors Affecting PeopleâA˘Zs Participation in Participatory Forest ´Management: The case of IFMP Adaba-Dodola in Bale zone of Oromia Region, 2003.
ViviRamdhani, Jaharuddin and E. H. Nugrahani, Dynamical System of Modelling theDepletion of Forestry Resources Due to Crowding by Industrialization, Applied Mathematical Sciences, Vol. 9, 2015, no. 82, 4067-4079.
Waleed K. Ahmed, Advantages and Disadvantages of Using MATLAB/ode45 for Solving Differential (3) Equations in Engineering Applications International Journal of Engineering (IJE), Volume (7): Issue (1): 2013.
KusumLata, Arvind Kumar Misra, Modeling the effect of economic efforts to control population pressure and conserve forestry resources June 19, 2017, Vol. 22, No. 4, 473–488 ISSN 1392-5113.
KusumLata, Arvind Kumar Misra, and Jang Bahadur Shukla. Modeling the effect of deforestation caused by human population pressure on wildlife species. 2018, Vol. 23, No. 3, 303–320 ISSN 1392-5113.
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