Juhua Liang

Sliding Bifurcations of Filippov Two Stage Pest Control Models with Economic Thresholds

In order to control pests, a specific management strategy called the threshold policy is proposed, which can be described by Filippov systems (or piecewise smooth systems). The aim of this work is to investigate a variety of bifurcation phenomena of the equilibria and sliding cycles of Filippov two stage structured population models with density dependent per capita birth rates and transition rates from the juvenile class into the adult class. It is shown that interadult competition alone can give rise to multiple sliding segments and multiple pseudoequilibria, whilst interadult and interjuvenile competition together can result in rich sliding bifurcations. As the threshold value varies, local sliding bifurcations including boundary node (saddle), tangency, and pseudo--saddle-node bifurcations occur sequentially, and global sliding bifurcations including buckling bifurcations of the sliding cycles, sliding crossing bifurcations, and pseudohomoclinic bifurcations can be present. Threshold policy control ha...

Threshold conditions for integrated pest management models with pesticides that have residual effects

Impulsive differential equations (hybrid dynamical systems) can provide a natural description of pulse-like actions such as when a pesticide kills a pest instantly. However, pesticides may have long-term residual effects, with some remaining active against pests for several weeks, months or years. Therefore, a more realistic method for modelling chemical control in such cases is to use continuous or piecewise-continuous periodic functions which affect growth rates. How to evaluate the effects of the duration of the pesticide residual effectiveness on successful pest control is key to the implementation of integrated pest management (IPM) in practice. To address these questions in detail, we have modelled IPM including residual effects of pesticides in terms of fixed pulse-type actions. The stability threshold conditions for pest eradication are given. Moreover, effects of the killing efficiency rate and the decay rate of the pesticide on the pest and on its natural enemies, the duration of residual effectiveness, the number of pesticide applications and the number of natural enemy releases on the threshold conditions are investigated with regard to the extent of depression or resurgence resulting from pulses of pesticide applications and predator releases. Latin Hypercube Sampling/Partial Rank Correlation uncertainty and sensitivity analysis techniques are employed to investigate the key control parameters which are most significantly related to threshold values. The findings combined with Volterra’s principle confirm that when the pesticide has a strong effect on the natural enemies, repeated use of the same pesticide can result in target pest resurgence. The results also indicate that there exists an optimal number of pesticide applications which can suppress the pest most effectively, and this may help in the design of an optimal control strategy.

Optimal dosage and economic threshold of multiple pesticide applications for pest control

Optimal timing (or Economic Threshold) and dosage of pesticide applications which maximize the profit function depend on many factors including pest population demography, crop susceptibility to damage and the rate at which a pesticide loses its toxicity. To analyze the effects of these factors on pest management, several pest control models with single and multiple treatments are presented by using impulsive differential equations. That is, pest control models with a single treatment and with multiple treatments of pesticides sprayed at fixed moments and unfixed moments (i.e. the model with an Economic Threshold) were investigated. In particular, choosing the maximum profits as the management objective, we investigated profit function directed at the problems of optimal timing of pesticide applications, Economic Threshold and optimal dosage of pesticides. Several sufficient conditions which guarantee the existences of optimum timing, dosage and Economic Threshold are provided. This approach can be used with more general models involving age structure of pest populations and the effects of stochastic factors.

Analytical methods for detecting pesticide switches with evolution of pesticide resistance

After a pest develops resistance to a pesticide, switching between different unrelated pesticides is a common management option, but this raises the following questions: (1) What is the optimal frequency of pesticide use? (2) How do the frequencies of pesticide applications affect the evolution of pesticide resistance? (3) How can the time when the pest population reaches the economic injury level (EIL) be estimated and (4) how can the most efficient frequency of pesticide applications be determined? To address these questions, we have developed a novel pest population growth model incorporating the evolution of pesticide resistance and pulse spraying of pesticides. Moreover, three pesticide switching methods, threshold condition-guided, density-guided and EIL-guided, are modelled, to determine the best choice under different conditions with the overall aim of eradicating the pest or maintaining its population density below the EIL. Furthermore, the pest control outcomes based on those three pesticide switching methods are discussed. Our results suggest that either the density-guided or EIL-guided method is the optimal pesticide switching strategy, depending on the frequency (or period) of pesticide applications.

Adaptive Release of Natural Enemies in a Pest-Natural Enemy System with Pesticide Resistance

Integrated pest management options such as combining chemical and biological control are optimal for combating pesticide resistance, but pose questions if a pest is to be controlled to extinction. These questions include (i) what is the relationship between the evolution of pesticide resistance and the number of natural enemies released? (ii) How does the cumulative number of natural enemies dying affect the number of natural enemies to be released? To address these questions, we developed two novel pest-natural enemy interaction models incorporating the evolution of pesticide resistance. We investigated the number of natural enemies to be released when threshold conditions for the extinction of the pest population in two different control tactics are reached. Our results show that the number of natural enemies to be released to ensure pest eradication in the presence of increasing pesticide resistance can be determined analytically and depends on the cumulative number of dead natural enemies before the next scheduled release time.

THE DYNAMICAL BEHAVIOR OF NON-SMOOTH SYSTEM WITH IMPULSIVE CONTROL STRATEGIES

Non-smooth system including impulsive strategies at both fixed and unfixed times are analyzed. For the model with fixed impulsive effects, the global stability of pest eradication periodic solution and the dominance of dynamic behavior are investigated. This indicates that the model with fixed moments has the potential to protect the natural enemies from extinction, but under some conditions may also serve to extinction of the pest. The second model is constructed according to the practices of IPM, that is, when the pest population reaches the economic injury level, a combination of biological, cultural, and chemical tactics that reduce pests to tolerable levels is used. Numerical investigations imply that there are several different types of periodic solutions and their maximum amplitudes are always less than the given economic threshold. The results also show that the time series at which the IPM strategies are applied are quite complex, which means that the application and realization of IPM in practice are very difficult.

Optimal Application Timing of Pest Control Tactics in Nonautonomous Pest Growth Model

Considering the effects of the living environment on growth of populations, it is unrealistic to assume that the growth rates of predator and prey are all constants in the models with integrated pest management (IPM) strategies. Therefore, a nonautonomous predator-prey system with impulsive effect is developed and investigated in the present work. In order to determine the optimal application timing of IPM tactics, the threshold value which guarantees the stability of pest-free periodic solution has been obtained firstly. The analytical formula of optimal application timings within a given period for different cases has been obtained such that the threshold value is the smallest, which is the most effective in successful pest control. Moreover, extensively numerical investigations have also been confirmed our main results and the biological implications have been discussed in more detail. The main results can guide the farmer to design the optimal pest control strategies.