Analysis of stability and Hopf bifurcation for an eco-epidemiological model with distributed delay

• Main Authors: Xueyong Zhou, Zhen Guo
• Format: Article
• Language: English
• Published: University of Szeged 2012-05-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: eco-epidemiological system; asymptotical stability; hopf bifurcation; distributed delay
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=1167

In this paper, the dynamical behavior of an eco-epidemiological model with distributed delay is studied. Sufficient conditions for the asymptotical stability of all the equilibria are obtained. We prove that there exists a threshold value of the infection rate $b$ beyond which the positive equilibrium bifurcates towards a periodic solution. We further analyze the orbital stability of the periodic orbits arising from bifurcation by applying Poore's condition. Numerical simulation with some hypothetical sets of data has been done to support the analytical findings.