A Mathematical Study on a Diseased Prey-Predator Model with Predator Harvesting
DOI:
https://doi.org/10.24203/ajfam.v8i2.6283Keywords:
Pre-predator model, Equilibrium points, Stability Analysis, Non-linear differential equationsAbstract
In this paper, we present a mathematical model for a prey-predator system with infectious disease in the prey population. We assumed that there is harvesting from the predator and a defensive property against predation. This model is constituted by a system of nonlinear decoupled ordinary first order differential equations, which describe the interaction among the healthy prey, infected prey and predator. The existence, uniqueness and boundedness of the system solutions are investigated. Local stability of the system at equilibrium points is discussed.
References
. M. R. May, Stability and Complexity in Model Ecosystems. Princeton, NJ: Princeton University, 1973.
. Kermack WO, Mc Kendrick AG. Contributions to the mathematical theory of epidemics, part1. Proceedings of the Royal Society of London Series A1927; 115:700–721.
. Anderson RM, May RM. The invasion, persistence and spread of infectious diseases within animal and plant communities. Philosophical Transactions of the Royal Society of London. Series B 1986; 314:533–570.
. Chattopadhyay J, Arino O. A predator–prey model with disease in the prey. Nonlinear Analysis 1999; 36:747–766.
. Z. Ma, F. Chen, C. Wu, and W. Chen, “Dynamic behaviors of a Lotka-Volterra predator-prey model incorporating a prey refuge and predator mutual interference,” Applied Mathematics and Computation, vol. 219, no. 15, pp. 7945–7953, 2013.
. P. J. Pal and P. K. Mandal, “Bifurcation analysis of a modified Leslie-Gower predator-prey model with Beddington-DeAngelis functional response and strong Allee effect,” Mathematics and Computers in Simulation, vol. 97, pp. 123–146, 2014.
. Raid Kamel Naji and Salam Jasim Majeed. The Dynamical Analysis of a Prey-Predator Model with a Refuge-Stage Structure Prey Population. International Journal of Differential Equations. Volume 2016, Article ID 2010464, 10 pages.
. Ahmed Sami Abdulghafour and Raid Kamel Naji. The impact of refuge and harvesting on the dynamics of prey-predator system. Sci. Int. (Lahore), 30 (2), 315-323. 2018
. D. Greenhalgh, Q. J. A. Khan, and F. I. Lewis, “Hopf bifurcation in two SIRS density dependent epidemic models,” Mathematical and Computer Modelling, vol. 39, no. 11-12, pp. 1261–1283, 2004.
. T. L. Zhang, J. L. Liu, and Z. D. Teng, “Stability of Hopf bifurcation of a delayed SIRS epidemic model with stage structure,” Nonlinear Analysis: Real World Applications, vol. 11, no. 1, pp. 293–306, 2010.
. Y. Z. Pei, S. Li, C. Li, and S. Chen, “The effect of constant and pulse vaccination on an SIR epidemic model with infectious period,” Applied Mathematical Modelling, vol. 35, no. 8, pp. 3866–3878, 2011.
. Raid Kamel Naji and Burhan Haqi Abdulateef. The dynamics of SICIR model with nonlinear incidence rate and saturated treatment function. Sci. Int. (Lahore), 29 (6), 1223-1236, 2017.
. S. Thota: Prey-Predator Model for Awash National Park, Oromia, Ethiopia and Its Stability Analysis with Simulations, Journal of Science and Sustainable Development, 7 (2) (2019), 15-21.
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