This paper presents infectious disease in prey-predator system. In the present work, a three Compartment mathematical eco-epidemiology model consisting of susceptible prey- infected prey and predator are formulated and analyzed. The positivity, boundedness, and existence of the solution of the model are proved. Equilibrium points of the models are identified. Local stability analysis of Trivial, Axial, Predator-free, and Disease-free Equilibrium points are done with the concept of Jacobian matrix and Routh Hourwith Criterion. Global Stability analysis of endemic equilibrium point of the model has been proved by defining appropriate Liapunove function. The basic reproduction number in this eco-epidemiological model obtained to be Ro=[β (μ3)2] ⁄ [qp2 (qp1Λ - μ1μ3)]. If the basic reproduction number Ro > 1, then the disease is endemic and will persist in the prey species. If the basic reproduction number Ro=1, then the disease is stable, and if basic reproduction number Ro < 1, then the disease is dies out from the prey species. Lastly, Numerical simulations are presented with the help of DEDiscover software to clarify analytical results.
| Published in | Mathematical Modelling and Applications (Volume 5, Issue 3) |
| DOI | 10.11648/j.mma.20200503.17 |
| Page(s) | 183-190 |
| 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. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Mathematical Ecoepidemiology, Prey- Predator System, Stability Analysis, Reproduction Number, Simulation Study
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APA Style
Abayneh Fentie Bezabih, Geremew Kenassa Edessa, Purnachandra Rao Koya. (2020). Mathematical Eco-Epidemiological Model on Prey-Predator System. Mathematical Modelling and Applications, 5(3), 183-190. https://doi.org/10.11648/j.mma.20200503.17
ACS Style
Abayneh Fentie Bezabih; Geremew Kenassa Edessa; Purnachandra Rao Koya. Mathematical Eco-Epidemiological Model on Prey-Predator System. Math. Model. Appl. 2020, 5(3), 183-190. doi: 10.11648/j.mma.20200503.17
AMA Style
Abayneh Fentie Bezabih, Geremew Kenassa Edessa, Purnachandra Rao Koya. Mathematical Eco-Epidemiological Model on Prey-Predator System. Math Model Appl. 2020;5(3):183-190. doi: 10.11648/j.mma.20200503.17
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Download@article{10.11648/j.mma.20200503.17,
author = {Abayneh Fentie Bezabih and Geremew Kenassa Edessa and Purnachandra Rao Koya},
title = {Mathematical Eco-Epidemiological Model on Prey-Predator System},
journal = {Mathematical Modelling and Applications},
volume = {5},
number = {3},
pages = {183-190},
doi = {10.11648/j.mma.20200503.17},
url = {https://doi.org/10.11648/j.mma.20200503.17},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20200503.17},
abstract = {This paper presents infectious disease in prey-predator system. In the present work, a three Compartment mathematical eco-epidemiology model consisting of susceptible prey- infected prey and predator are formulated and analyzed. The positivity, boundedness, and existence of the solution of the model are proved. Equilibrium points of the models are identified. Local stability analysis of Trivial, Axial, Predator-free, and Disease-free Equilibrium points are done with the concept of Jacobian matrix and Routh Hourwith Criterion. Global Stability analysis of endemic equilibrium point of the model has been proved by defining appropriate Liapunove function. The basic reproduction number in this eco-epidemiological model obtained to be Ro=[β (μ3)2] ⁄ [qp2 (qp1Λ - μ1μ3)]. If the basic reproduction number Ro > 1, then the disease is endemic and will persist in the prey species. If the basic reproduction number Ro=1, then the disease is stable, and if basic reproduction number Ro < 1, then the disease is dies out from the prey species. Lastly, Numerical simulations are presented with the help of DEDiscover software to clarify analytical results.},
year = {2020}
}
TY - JOUR T1 - Mathematical Eco-Epidemiological Model on Prey-Predator System AU - Abayneh Fentie Bezabih AU - Geremew Kenassa Edessa AU - Purnachandra Rao Koya Y1 - 2020/08/20 PY - 2020 N1 - https://doi.org/10.11648/j.mma.20200503.17 DO - 10.11648/j.mma.20200503.17 T2 - Mathematical Modelling and Applications JF - Mathematical Modelling and Applications JO - Mathematical Modelling and Applications SP - 183 EP - 190 PB - Science Publishing Group SN - 2575-1794 UR - https://doi.org/10.11648/j.mma.20200503.17 AB - This paper presents infectious disease in prey-predator system. In the present work, a three Compartment mathematical eco-epidemiology model consisting of susceptible prey- infected prey and predator are formulated and analyzed. The positivity, boundedness, and existence of the solution of the model are proved. Equilibrium points of the models are identified. Local stability analysis of Trivial, Axial, Predator-free, and Disease-free Equilibrium points are done with the concept of Jacobian matrix and Routh Hourwith Criterion. Global Stability analysis of endemic equilibrium point of the model has been proved by defining appropriate Liapunove function. The basic reproduction number in this eco-epidemiological model obtained to be Ro=[β (μ3)2] ⁄ [qp2 (qp1Λ - μ1μ3)]. If the basic reproduction number Ro > 1, then the disease is endemic and will persist in the prey species. If the basic reproduction number Ro=1, then the disease is stable, and if basic reproduction number Ro < 1, then the disease is dies out from the prey species. Lastly, Numerical simulations are presented with the help of DEDiscover software to clarify analytical results. VL - 5 IS - 3 ER -
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