Integrated pest management models and their dynamical behaviour

Abstract

Two impulsive models of integrated pest management (IPM) strategies are proposed, one with fixed intervention times and the other with these unfixed. The first model allows natural enemies to survive but under some conditions may lead to extinction of the pest. We use a simple prey-dependent consumption model with fixed impulsive effects and show that there exists a globally stable pest-eradication periodic solution when the impulsive period is less than certain critical values. The effects of pest resistance to pesticides are also studied. The second model is constructed in the light of IPM practice such that when the pest population reaches the economic injury level (EIL), a combination of biological, cultural, and chemical tactics that reduce pests to tolerable levels is invoked. Using analytical methods, we show that there exists an orbitally asymptotically stable periodic solution with a maximum value no larger than the given Economic Threshold (ET). The complete expression for this periodic solution is given and the ET is evaluated for given parameters. We also show that in some cases control costs can be reduced by replacing IPM interventions at unfixed times with periodic interventions. Further, we show that small perturbations of the system do not affect the existence and stability of the periodic solution. Thus, we provide the first demonstration using mathematical models that an IPM strategy is more effective than classical control methods.

Sliding Bifurcation Analysis and Global Dynamics for a Filippov Predator-prey System

“…However, it is shown that biological control is more popular in reality, and it also affects the development and extinction of the prey population [23,26]. The more comprehensive analysis for Filippov system (1.4) with the effects of both chemical and biological control will be studied in the future.…”

“…It is interesting to note that none of the models proposed above incorporate the control strategies into the non-smooth Gause model [16,17,24,32]. In reality, however, if the variable x(t) in system (1.3) represents the pest population, then the pest population may cause harms to crops once the density of the pest reaches and exceeds the economic threshold [23,26]. Therefore, control strategies such as chemical control, biological control or their combinations should be implemented when the density of the pest reaches the economic threshold.…”

Analytical methods for detecting pesticide switches with evolution of pesticide resistance

“…Recently, many mathematical models with impulsive chemical control tactics and releases of natural enemies have been proposed to model an IPM strategy such as spraying of pesticides [25,[28][29][30][31][32][33] or releases of natural enemies at critical times [27,[34][35][36][37][38][39][40][41]. Those studies mainly focused on the effects of chemical control and biological control on the permanence or extinction of pest populations, and did not consider the effects of pesticide resistance.…”

Integrated Pest Management and Spatial Structure

“…By using models, it is possible to understand better the processes that govern biological systems of pest insects, because they describe very well the complexity involved in the population dynamics of species from simple assumptions incorporated in the theoretical formalism (Faria & Godoy, 2001;Serra et al, 2007). In the 1980s, IPM principles began to be used to control insect populations in urban sites, such as schools, parks, hospitals, and nursing homes; and following these ideas, in the 1990s mathematical models began to be constructed to analyze and discuss IPM methods in a more qualitative and quantitative way (Lima et al, 2009;Tang et al, 2005;Tang & Cheke, 2008). In particular, Tang and coworkers demonstrated a stable periodic solution in a prey-dependent consumption model with fixed impulsive effects, and gave an analytical expression for the period of this periodic solution.…”

“…In particular, Tang and coworkers demonstrated a stable periodic solution in a prey-dependent consumption model with fixed impulsive effects, and gave an analytical expression for the period of this periodic solution. This period plays an important role in pest control, because it can be used to alter an IPM strategy with unfixed times for interventions, to one with periodic interventions, thus minimizing the cost of pest monitoring (Tang et al, 2005).…”