Search

This paper investigates the optimal impulsive management of pest growth model aiming at minimizing the amount of pests at the terminal time. By means of time-scaling and time translation transformation techniques, the gradient formulas of the cost function with respect to impulsive releasing amount and timing of natural enemies are given for three cases such as the amount control, the timing control and the mixed control. Based on the gradient formulas and the designed algorithm, we find the optimal impulsive releasing times and amounts of enemies by numerical simulations. And the mixed control strategy is illustrated to be the best strategy through comparing the three optimal control strategies with the same initial control parameters. In addition, simulations indicate that the optimization of governance policies may increase the periodic oscillation amplitude of populations, but ultimately it will reduce the amount of pests and lower the cost. Furthermore, our optimal biological interference strategies are superior to those in many literatures in which the enemy is released by the fixed amount at the fixed time. [ABSTRACT FROM AUTHOR]

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: Considering the impact of harvesting on the coexistence and competitive exclusion of competitive predators, a two-zooplankton one-phytoplankton model with harvesting is proposed and investigated. First, stability criteria of the model is analyzed both from local and global point of view. Second, two types of zooplankton will competitively exclude each other in the absence of harvesting with the zooplankton with the larger threshold persisting. If harvest rates are discriminate, then a dominant zooplankton may occur depending on the harvesting level. Thus, for some harvesting levels, the zooplankton one may persist while for other harvesting levels zooplankton two may persist. Furthermore, the value of the harvesting level and coexistence line are obtained when coexistence occur. Finally, the impact of harvesting is mentioned along with numerical results to provide some support to the analytical findings. [Copyright &y& Elsevier]

Abstract: In this paper, two SIR epidemic models with different patterns of recruitment and difference in immunity are investigated. When the recruitment rate is less than some threshold value, the disease will be eradicated. Furthermore, for the continuous recruitment model, according to the Poincare–Bendixson theorem, the global asymptotical stability of a unique positive equilibrium is obtained. For the pulse recruitment model, we investigated the existence of nontrivial periodic solutions via a supercritical (subcritical) bifurcation. From a biological point of view, our results indicate that (1) the disease can be eradicated if the recruitment rate is controlled under some threshold; (2) the number of the infected increases as the difference in immunity increases; (3) fewer individuals are infected as the pulse recruitment is taken, displaying its effect on the control of the disease. [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: 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]

Abstract: Three different vaccination and treatment strategies in the SIR epidemic model with saturated infectious force and vertical transmission are analyzed. The dynamics of epidemic models are globally investigated by using Floquet theory and comparison theorem of impulsive differential equation. Thresholds are identified and global stability results are proved. For every treatment and vaccination strategy, the disease-free periodic solution of impulsive system has been obtained and is found to be globally asymptotically stable when the basic reproduction number is less than one, equivalently the cure rate is larger than the threshold value, whereas the disease is persistent when the basic reproduction number is larger than one. These results indicate that a large cure rate will lead to the eradication of a disease. [Copyright &y& Elsevier]

Abstract: Considering that some phytoplankton and zooplankton are harvested for food, a phytoplankton–zooplankton model with harvesting is proposed and investigated. First, stability conditions of equilibria and existence conditions of a Hopf-bifurcation are established. Our results indicate that over exploitation would result in the extinction of the population and an appropriate harvesting strategy should ensure the sustainability of the population which is in line with reality. Furthermore, the existence of bionomic equilibria and the optimal harvesting policy are discussed. The present value of revenues is maximized by using Pontryagin’s maximum principle subject to the state equations and the control constraints. We discussed the case of optimal equilibrium solution. It is found that the shadow prices remain constant over time in optimal equilibrium when they satisfy the transversality condition. It is established that the zero discounting leads to the maximization of economic revenue and that an infinite discount rate leads to complete dissipation of economic rent. Finally, some numerical simulations are given to illustrate our results. [ABSTRACT FROM AUTHOR]

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]