American Journal of Applied Mathematics

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Modeling and Simulation Study of the Population Dynamics of Commensal-Host-Parasite System

Received: Apr. 30, 2018    Accepted: Jun. 01, 2018    Published: Jul. 05, 2018
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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.

DOI 10.11648/j.ajam.20180603.11
Published in American Journal of Applied Mathematics ( Volume 6, Issue 3, June 2018 )
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), 2024. Published by Science Publishing Group

Keywords

Commensalism, Parasite, Stability, Eco-epidemiology, Numerical Simulation

References
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[2] AlyssaLois M. (2016). Non-native parasite enhances susceptibility of host to native predators, Springer-Verlag, Berlin, Heidelberg.
[3] R. Bhattacharyya, and B. Mukhopadhyay, on an eco-epidemiological model with prey harvesting and predator switching: local and global perspectives, Nonlinear Anal.: RWA 11 (2010) 3824.
[4] Hassell M. P. and May R. M. Stability in insect host-parasite models. J. Animal. Ecol.42, 693–726 (1973).
[5] Hatcher M. J., Dick J. T. A., Dunn A. M. (2012). Disease emergence and invasions. Funct Ecol 26:1275–1287.
[6] E. Venturino. The influence of diseases on Lotka–Volterra systems, Rocky Mt. J. Math. 24(1994) 381–402.
[7] P. J. Hudson, and A. P. Dobson, D. Newborn, Do parasites make Prey more vulnerable to predation?Red-grouse and parasites, J. Anim. Ecol. 61 (1992) 681–692.
[8] M. Haque, and E. Venturino, Modelling disease spreading in symbiotic communities, Wildlife: Destruction, Conservation and Biodiversity, Nova Science Publishers, USA, 2009.
[9] Sule H., Muhamad, R., and Omar D. Parasitism rate, host stage preference and functional response of Tamarixiaradiata on Diaphorinacitri. Int. J. Agric. Biol. 16 (2014) 783–788.
[10] J. H. P. Dawes and M. O. Souza (2013). A derivation of Hollings type I, II and III functional responses in predator-prey systems, 327, 11-22.
[11] Poulin R (2007). Evolutionary Ecology of Parasites, 2ed, Princeton University Press, Princeton.
[12] Fanghong Zhang and Cuncheng Jin. Analysis of an eco-epidemiological model with Disease in the prey and predator. (2017) 73-79.
[13] Sen P., Das k. Simultaneous Effects of Prey Defence and Predator Infection on a Predator Prey System. Ann. Bio. Sci., 2017, 5 (1):37-46
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[15] Auld S. K. J. R., Hall S. R. & Duffy M. A. Epidemiology of a Daphnia-multi parasite system and its implications for the Red Queen. (2012).
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[17] Jean Jules Tewa. Mathematical analysis of two-patch model of tuberculosis disease with staged progression, Appl. Math. Model. 36 (2012) 5792–5807.
[18] Chakra M. A., Hil be, C. and Treutlen A. Plastic behaviors in hosts promote the emergence of retaliatory parasites, Sci. Rep. 4, 4251 (2014).
[19] Eswarappa S. M., Estrela S. & Brown S. P. Within-host dynamics of multi-species infections: Facilitation, competition and virulence. (2012).
[20] Tompkins D. M., White A. R. & Boots M. Ecological replacement of native red squirrels by invasive greys driven by disease. Ecol. Lett. 6, 189–196 (2003).
[21] Geremew K, N. Phani Kumar, Boka K. Dynamics of Commensalism Interaction with Linear and Holling Type II Functional Responses by the Host to the Commensal Species, (2017) 23-34.
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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

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    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

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    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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  • @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://download.sciencepg.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}
    }
    

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    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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Author Information
  • Department of Mathematics, Wollega University, Nekemte, Ethiopia

  • Department of Mathematics, Wollega University, Nekemte, Ethiopia

  • Department of Mathematics, Hawassa University, Hawassa, Ethiopia

  • Section