Influence of Intrapredatory Interferences on Impulsive Biological Control Efficiency

Dynamic analysis and control of a rice-pest system under transcritical bifurcations

A decision model is developed by adopting two control techniques, combining cultural methods and pesticides in a hybrid approach. To control the adverse effects in the long term and to be able to evaluate the extensive use of pesticides on the environment and nearby ecosystems, the novel decision model assumes the use of pesticides only in an emergency situation. We, therefore, formulate a rice-pest-control model by rigorously modelling a rice-pest system and including the decision model and control techniques. The model is then extended to become an optimal control system with an objective function that minimizes the annual losses of rice by controlling insect pest infestations and simultaneously reduce the adverse impacts of pesticides on the environment and nearby ecosystems. This rice-pest-control model is verified by analysis, obtains the necessary conditions for optimality, and confirms our main results numerically. The rice-pest system is verified by stability analysis at equilibrium points and shows transcritical bifurcations indicative of acceptable thresholds for insect pests to demonstrate the pest control strategy.

Theoretical study and control optimization of an integrated pest management predator-prey model with power growth rate

This work presents a pest control predator-prey model, where rate of change in prey density follows a scaling law with exponent less than one and the control is by an integrated management strategy. The aim is to investigate the change in system dynamics and determine a pest control level with minimum control price. First, the dynamics of the proposed model without control is investigated by taking the exponent as an index parameter. And then, to determine the frequency of spraying chemical pesticide and yield releases of the predator, the existence of the order-1 periodic orbit of the control system is discussed in cases. Furthermore, to ensure a certain robustness of the adopted control, i.e., for an inaccurately detected species density or a deviation, the control system could be stabilized at the order-1 periodic orbit, the stability of the order-1 periodic orbit is verified by an stability criterion for a general semi-continuous dynamical system. In addition, to minimize the total cost input in pest control, an optimization problem is formulated and the optimum pest control level is obtained. At last, the numerical simulations with a specific model are carried out to complement the theoretical results.

Biocontrol in an impulsive predator-prey model

We study a model for biological pest control (or "biocontrol") in which a pest population is controlled by a program of periodic releases of a fixed yield of predators that prey on the pest. Releases are represented as impulsive increases in the predator population. Between releases, predator-pest dynamics evolve according to a predator-prey model with some fairly general properties: the pest population grows logistically in the absence of predation; the predator functional response is either of Beddington-DeAngelis type or Holling type II; the predator per capita birth rate is bounded above by a constant multiple of the predator functional response; and the predator per capita death rate is allowed to be decreasing in the predator functional response and increasing in the predator population, though the special case in which it is constant is permitted too. We prove that, when the predator functional response is of Beddington-DeAngelis type and the predators are not sufficiently voracious, then the biocontrol program will fail to reduce the pest population below a particular economic threshold, regardless of the frequency or yield of the releases. We prove also that our model possesses a pest-eradication solution, which is both locally and globally stable provided that predators are sufficiently voracious and that releases occur sufficiently often. We establish, curiously, that the pest-eradication solution can be locally stable whilst not being globally stable, the upshot of which is that, if we delay a biocontrol response to a new pest invasion, then this can change the outcome of the response from pest eradication to pest persistence. Finally, we state a number of specific examples for our model, and, for one of these examples, we corroborate parts of our analysis by numerical simulations.

An impulsively controlled pest management model with n predator species and a common prey

This paper investigates the dynamics of a competitive single-prey n-predators model of integrated pest management, which is subject to periodic and impulsive controls, from the viewpoint of finding sufficient conditions for the extinction of prey and for prey and predator permanence. The per capita death rates of prey due to predation are given in abstract, unspecified forms, which encompass large classes of death rates arising from usual predator functional responses, both prey-dependent and predator-dependent. The stability and permanence conditions are then expressed as balance conditions between the cumulative death rate of prey in a period, due to predation from all predator species and to the use of control, and to the cumulative birth rate of prey in the same amount of time. These results are then specialized for the case of prey-dependent functional responses, their biological significance being also discussed.