Abstract
This paper presents the mathematical analysis of the dynamical system for avian influenza. The proposed model considers a nonlinear dynamical model of birds and human. The half-saturated incidence rate is used for the transmission of avian influenza infection. Rigorous mathematical results are presented for the proposed models. The local and global dynamics of each model are presented and proven that when R-0 < 1, then the disease-free equilibrium of each model is stable both locally and globally, and when R-0 > 1, then the endemic equilibrium is stable both locally and globally. The numerical results obtained for the proposed model shows that influenza could be eliminated from the community if the threshold is not greater than unity.