A pest management SI model with periodic biological and chemical control concern

Abstract In this work, we consider an SI model for pest management, with concerns about impulsive releases of infective pests and pesticides sprays. We prove that all solutions of (I) S ′ ( t ) = rS ( t ) 1 - S ( t ) + θ I ( t ) K - β S ( t ) I 2 ( t ) , t ≠ n τ , I ′ ( t ) = β S ( t ) I 2 ( t ) - wI ( t ) , t ≠ n τ , Δ S ( t ) = - μ 1 S ( t ) , t = n τ , Δ I ( t ) = - μ 2 I ( t ) + μ , t = n τ , n = 1 , 2 , … , are uniformly ultimately bounded and there exists globally asymptotic stability periodic solution of pest-extinction when ln 1 1 - μ 1 > r τ - r μ θ ( 1 - exp ( - w τ ) ) Kw ( 1 - ( 1 - μ 2 ) exp ( - w τ ) ) - β μ 2 ( 1 - exp ( - 2 w τ ) ) 2 w ( 1 - ( 1 - μ 2 ) exp ( - w τ ) ) 2 is satisfied, and the condition for permanence of system (I) is also obtained. It is concluded that the approach of combining impulsive infective releasing with impulsive pesticide spraying provides reliable tactic basis for practical pest management.