An appropriate pest management SI model with biological and chemical control concern

Abstract In this work, we consider an SI model for pest management, and concern about releasing infective pests and spraying pesticides at different fixed moments. We prove that all solutions of (*) d S ( t ) d t = rS ( t ) 1 - S ( t ) + θ I ( t ) K - β S ( t ) I ( t ) , t ≠ ( n + l - 1 ) τ , t ≠ n τ , d I ( t ) d t = β S ( t ) I ( t ) - wI ( t ) , t ≠ ( n + l - 1 ) τ , t ≠ n τ , ▵ S ( t ) = - μ 1 S ( t ) , t = ( n + l - 1 ) τ , ▵ I ( t ) = - μ 2 I ( t ) , t = ( n + l - 1 ) τ , ▵ S ( t ) = 0 , t = n τ , ▵ I ( t ) = μ , t = n τ , 0 l 1 , n = 1 , 2 … , are uniformly ultimately bounded. The conditions of the globally asymptotic stability pest-extinction boundary periodic solution and the permanence of system (*) are also obtained. Our results provide reliable tactic basis for the practical pest management.

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