We analyze and formulate an Eco-Epidemiological model with disease in the prey and predator, study the existence of the non-negative equilibria, obtain the sufficient conditions of locally asymptotical stability of the equilibria, then analyze the global stability of the positive equilibria.
This study contributes in the existing literature of Eco-Epidemiological model. We get the conditions of local asymptotic and the existence of the boundary balance, and we proved the positive balance point is global asymptotical stability by constructing Liapunov function.
Y. Jianya and Z. Fengqing, "The prey-predator model with epidemic in the predator [J]," Mathematical Bioscien, vol. 22, pp. 419-423, 2007. View at Google Scholar
Z. Wuzhong and Z. Fengqing, "A prey-predator SIS model with epidemic in the predator [J]," Xuzhou Noraml Univ, vol. 26, pp. 132-133, 2008.
S. Shulin and Y. Cunde, "Analysis of eco-epidemiological SIS model with epidemmic in the predator [J]," Chinese Journal of Engineering, vol. 22, pp. 30-31, 2005. View at Google Scholar
H. W. Herbert, W. Wendi, H. Litao, and M. Zhien, "A predator-prey model with infected prey [J]," Theoretical Population Biology, vol. 66, pp. 259-268, 2004. View at Google Scholar
X. Yanni and C. Lansun, "A ratio-dependent predator-prey model with disease in the prey [J]," Applied Mathematics and Computation, vol. 131, pp. 397-414, 2002. View at Google Scholar | View at Publisher