Stability of a Model of Nonlinear Forest Insect Pests

摘要

Based on the classical epidemic mode, a new epidemic model of forest which integrates Monochamus Alternatus Hope with Pines was established. The expression of the critical threshold was found. It is proved that, when the critical threshold less than 1, the disease free equilibrium is locally asymptotically stable, and when the critical threshold more than 1, the insect pests equilibrium is locally asymptotically stable. In addition to, the limit cycle of this model is non existent.