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J. Korean Math. Soc. 2009; 46(4): 713-731
Printed July 1, 2009
https://doi.org/10.4134/JKMS.2009.46.4.713
Copyright © The Korean Mathematical Society.
Analysis of a delay prey-predator model with disease in the prey species only
Xueyong Zhou, Xiangyun Shi, and Xinyu Song
Xinyang Normal University
In this paper, a three-dimensional eco-epidemiological model with delay is considered. The stability of the two equilibria, the existence of Hopf bifurcation and the permanence are investigated. It is found that Hopf bifurcation occurs when the delay $\tau$ passes though a sequence of critical values. The estimation of the length of delay to preserve stability has also been calculated. Numerical simulation with a hypothetical set of data has been done to support the analytical findings.
Keywords: predator-prey model, eco-epidemiology, delay, Hopf bifurcation
MSC numbers: 92D25, 92D30, 34K18, 34K20
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