This paper deals with the modeling and simulation study of Commensal-host species system together with the inclusion of parasite population. The model comprises of three populations viz. Host, Commensal and Parasite. The Commensal population gets benefit from Host population but the former do not do any harm to the latter. The parasite population gets benefit and also do harm to Host population. However, the Commensal population only harms the parasites. The mathematical model is comprised of a system of three first order non-linear ordinary differential equations. Mathematical analysis of the model is conducted. Positivity and boundedness of the solution have been verified and thus shown that the model is physically meaningful and biologically acceptable. Scaled model is constructed so as to reduce the number of model parameters. Equilibrium points of the model are identified and stability analysis is conducted. Simulation study is conducted in order to support the mathematical analysis. In the present model the Commensal population lies higher and the parasite population lies below respectively the host population. This fact is well supported by the mathematical analysis as well as simulation study. The results of analysis and simulation are presented and discussed lucidly in the text of the paper.
| Published in | American Journal of Applied Mathematics (Volume 6, Issue 3) |
| DOI | 10.11648/j.ajam.20180603.11 |
| Page(s) | 97-108 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2018. Published by Science Publishing Group |
Commensalism, Parasite, Stability, Eco-epidemiology, Numerical Simulation
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APA Style
Geremew Kenassa Edessa, Boka Kumsa, Purnachandra Rao Koya. (2018). Modeling and Simulation Study of the Population Dynamics of Commensal-Host-Parasite System. American Journal of Applied Mathematics, 6(3), 97-108. https://doi.org/10.11648/j.ajam.20180603.11
ACS Style
Geremew Kenassa Edessa; Boka Kumsa; Purnachandra Rao Koya. Modeling and Simulation Study of the Population Dynamics of Commensal-Host-Parasite System. Am. J. Appl. Math. 2018, 6(3), 97-108. doi: 10.11648/j.ajam.20180603.11
AMA Style
Geremew Kenassa Edessa, Boka Kumsa, Purnachandra Rao Koya. Modeling and Simulation Study of the Population Dynamics of Commensal-Host-Parasite System. Am J Appl Math. 2018;6(3):97-108. doi: 10.11648/j.ajam.20180603.11
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Download@article{10.11648/j.ajam.20180603.11,
author = {Geremew Kenassa Edessa and Boka Kumsa and Purnachandra Rao Koya},
title = {Modeling and Simulation Study of the Population Dynamics of Commensal-Host-Parasite System},
journal = {American Journal of Applied Mathematics},
volume = {6},
number = {3},
pages = {97-108},
doi = {10.11648/j.ajam.20180603.11},
url = {https://doi.org/10.11648/j.ajam.20180603.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20180603.11},
abstract = {This paper deals with the modeling and simulation study of Commensal-host species system together with the inclusion of parasite population. The model comprises of three populations viz. Host, Commensal and Parasite. The Commensal population gets benefit from Host population but the former do not do any harm to the latter. The parasite population gets benefit and also do harm to Host population. However, the Commensal population only harms the parasites. The mathematical model is comprised of a system of three first order non-linear ordinary differential equations. Mathematical analysis of the model is conducted. Positivity and boundedness of the solution have been verified and thus shown that the model is physically meaningful and biologically acceptable. Scaled model is constructed so as to reduce the number of model parameters. Equilibrium points of the model are identified and stability analysis is conducted. Simulation study is conducted in order to support the mathematical analysis. In the present model the Commensal population lies higher and the parasite population lies below respectively the host population. This fact is well supported by the mathematical analysis as well as simulation study. The results of analysis and simulation are presented and discussed lucidly in the text of the paper.},
year = {2018}
}
TY - JOUR T1 - Modeling and Simulation Study of the Population Dynamics of Commensal-Host-Parasite System AU - Geremew Kenassa Edessa AU - Boka Kumsa AU - Purnachandra Rao Koya Y1 - 2018/07/05 PY - 2018 N1 - https://doi.org/10.11648/j.ajam.20180603.11 DO - 10.11648/j.ajam.20180603.11 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 97 EP - 108 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20180603.11 AB - This paper deals with the modeling and simulation study of Commensal-host species system together with the inclusion of parasite population. The model comprises of three populations viz. Host, Commensal and Parasite. The Commensal population gets benefit from Host population but the former do not do any harm to the latter. The parasite population gets benefit and also do harm to Host population. However, the Commensal population only harms the parasites. The mathematical model is comprised of a system of three first order non-linear ordinary differential equations. Mathematical analysis of the model is conducted. Positivity and boundedness of the solution have been verified and thus shown that the model is physically meaningful and biologically acceptable. Scaled model is constructed so as to reduce the number of model parameters. Equilibrium points of the model are identified and stability analysis is conducted. Simulation study is conducted in order to support the mathematical analysis. In the present model the Commensal population lies higher and the parasite population lies below respectively the host population. This fact is well supported by the mathematical analysis as well as simulation study. The results of analysis and simulation are presented and discussed lucidly in the text of the paper. VL - 6 IS - 3 ER -
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