Modeling and Stability Analysis of Host-parasite Population Dynamics
Mathematical Modelling and Applications
Volume 5, Issue 2, June 2020, Pages: 118-128
Received: Jan. 1, 2020; Accepted: May 5, 2020; Published: May 28, 2020
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Authors
Geremew Kenassa Edessa, Department of Mathematics, Wollega University, Nekemte, Ethiopia
Purnachandra Rao Koya, Department of Mathematics, Wollega University, Nekemte, Ethiopia
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Abstract
In this study, a mathematical model is developed to explore the population dynamics of two host species. Both the hosts depend on the same resources and the availability of such resources is limited in nature. If the host populations increase abnormally the limited natural resources will be used up. Hence, the concept of parasite is brought in to the picture to regulate the host populations. The parasite is a mechanism that reduces the host populations. However, on one hand if the parasite attacks more the hosts may extinct and on the other hand if the parasite do not attack then the host populations may increase and resource may be used up. Hence, the parasite is expected to maintain a balance so that neither the host populations nor the resources extinct. Here, both the hosts are classified in to susceptible and infected and hence the model comprises of four populations: Susceptible Host–1, Infected Host–1, Susceptible Host–2 and Infected Host–2. Thus, the mathematical model comprises of a system of four 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. Equilibrium points of the model are identified and stability analysis is conducted. Simulation study is conducted in order to support the mathematical analysis using software packages Mat lab and DeDiscover.
Keywords
Modeling, Hosts, Parasite-mediated Interactions, Stability, Numerical Simulation
To cite this article
Geremew Kenassa Edessa, Purnachandra Rao Koya, Modeling and Stability Analysis of Host-parasite Population Dynamics, Mathematical Modelling and Applications. Vol. 5, No. 2, 2020, pp. 118-128. doi: 10.11648/j.mma.20200502.17
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Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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