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Abstract: Taking into account periodic impulsive biological and chemical control for pest management at different fixed moment, a three species prey–predator system with Holling type II functional response was investigated. By using Floquet’s theory and the small amplitude perturbation method, it was obtained that there exists an asymptotically stable preys-eradication periodic solution when the impulsive period is less than some critical minimum value (or the release amount of the predator is larger than some critical maximum value), and the system is permanent under the conditions that both the insecticidal effect and impulsive period are grater than some critical maximum values. Furthermore, it is obtained that IPM is more effective than any single one after comparison. Finally, numerical simulations are carried on to show the complex dynamic behavior of system. [Copyright &y& Elsevier]

Abstract: In this paper, two integrated pest management models are investigated, which rely on release of infective pest individuals and of natural enemies in a constant amount, together with spraying of pesticides. It is proved that the susceptible pests can be eradicated if the release amount of infected pests is above some threshold or the pesticide effect is above another threshold. Furthermore, permanent conditions are established when an impulsive control is used. Finally, numerical results show that (1) fewer infected pests or pesticides are needed as the impulsive strategy is taken, displaying its positive effect on the pest control; (2) our assumption that the natural enemies of the pests do not catch the infective pests would reduce the level of the susceptible pests. [Copyright &y& Elsevier]

Abstract: A delayed SEIQR epidemic model with pulse vaccination and the quarantine measure is investigated. Using the discrete dynamical system determined by the stroboscopic map, we obtain the exact periodic disease-free solution. Using the comparison method, we prove that the disease-free periodic solution is globally attractive when the basic reproductive number () is less than unity, and that the disease is permanent when another basic reproductive number () is greater than unity. In other words, the disease will be extinct if the pulse vaccination rate is larger than a critical value and the disease will be uniformly persistent if the vaccination rate is less than another critical value . Our results indicate that a longer latent period of the disease or a larger pulse vaccination rate will lead to the eradication of the disease, and whether the disease will be extinct or not is independent of the removal rate from the quarantined group. Furthermore, a larger fraction of susceptibles should be vaccinated against the disease unless the quarantine measure is taken. Finally, we find that the number of the infected decreases as the quarantine measure is taken. We carry out numerical simulations to verify our results. [Copyright &y& Elsevier]

Abstract: An impulsive delayed SI model with variable coefficients and a nonlinear incidence is formulated and analyzed. By introducing three thresholds, we obtain sufficient conditions for eradication and permanence of the disease, respectively. It is shown that the conditions depend on time delay for both the global attractivity of the positive infection-free periodic solution and permanence of the model. Furthermore, our results indicate that the disease will disappear if the ratio of the maximum to minimum of the pulse vaccination rate is lager than some value. The main feature of this paper is that we introduce multi-delays and variable coefficients into the SI model, and exhibit a new method which is applied to investigate this model. Numerical results show that the system we considered has complex dynamics including periodic and quasi-periodic oscillations. [Copyright &y& Elsevier]