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

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 ofequation(I)S′(t)=rS(t)1-S(t)+θI(t)K-βS(t)I2(t),t≠nτ,I′(t)=βS(t)I2(t)-wI(t),t≠nτ,ΔS(t)=-μ1S(t),t=nτ,ΔI(t)=-μ2I(t)+μ,t=nτ,n=1,2,…,are uniformly ultimately bounded and there exists globally asymptotic stability periodic solution of pest-extinction when ln11-μ1>rτ-rμθ(1-exp(-wτ))Kw(1-(1-μ2)exp(-wτ))-βμ2(1-exp(-2wτ))2w(1-(1-μ2)exp(-wτ))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.