Stability of The Endemic Equilibrium of A Forest Insect Pest Discrete Model

In this paper, the discrete model of forest insect pests is discussed. Firstly, according to characteristics of the spread of forest insect pests, a discrete-time model with difference equations to reflect the situation that tree diseases did not diffuse across different patches is built. Secondly, the equilibrium points of the system are discussed and the stability of the endemic equilibrium is analyzed. In addition, the sufficient conditions for stability of endemic equilibrium are given and then it has been shown that if the infection rate of each patch is constant under certain conditions, the number of infected trees can be controlled in a certain range.