Two Generalized Predator-Prey Models for Integrated Pest Management with Stage Structure and Disease in the Prey Population

and Applied Analysis 3 where we denote P = {1, 2, . . . , p} and P 1 = {1, 2, . . . , p − 1} throughout the paper. Case 2. Natural enemies releases are more frequent than the release of the infective pests. We release the infective pests impulsively with releasing amount q 1 . Assume that τ n+1 − τ n ≡ T k holds for all n ∈ Z + , where T k is the period of releasing the infective pests. During the period, p times of natural enemy releases are applied. That is, there exists an integer p, such that 0 < λ 1 < λ 2 < λ 3 ⋅ ⋅ ⋅ < λ p < T k . For the simplicity of calculation and research, we assume that λ 1 = λ 2 − λ 1 = λ 3 − λ 2 = ⋅ ⋅ ⋅ = T k − λ p . Accordingly, the mathematical model will be