ECONOMIC THRESHOLDS: AN APPLICATION TO FLORICULTURE

This paper introduces conjunctive optimal pest management and production decision rules applied to the floriculture industry. A grower is faced with optimally controlling multiple pests and applying cultural controls to maximize the expected net present value of benefits within a discrete time framework, subject to biological and marketing constraints.Crop Production/Industries,

Modeling and control of complex dynamic systems: Applied mathematical aspects

The concept of complex dynamic systems arises in many varieties, including the areas of energy generation, storage and distribution, ecosystems, gene regulation and health delivery, safety and security systems, telecommunications, transportation networks, and the rapidly emerging research topics seeking to understand and analyse. Such systems are often concurrent and distributed, because they have to react to various kinds of events, signals, and conditions. They may be characterized by a system with uncertainties, time delays, stochastic perturbations, hybrid dynamics, distributed dynamics, chaotic dynamics, and a large number of algebraic loops. This special issue provides a platform for researchers to report their recent results on various mathematical methods and techniques for modelling and control of complex dynamic systems and identifying critical issues and challenges for future investigation in this field. This special issue amazingly attracted one-hundred-and eighteen submissions, and twenty-eight of them are selected through a rigorous review procedure

OPTIMAL PEST CONTROL IN FLORICULTURE PRODUCTION OF ORNAMENTAL CROPS

We develop a conceptual bioeconomic model of floriculture production, wherein optimal decision rules depend on an intertemporal economic objective to maximize profits subject to economic and biological processes. The necessary conditions highlight intertemporal tradeoffs between aesthetic benefits and expected future net benefits of insect stocks, which have important policy implications.Research Methods/ Statistical Methods,

The effects of resource limitation on a predator-prey model with control measures as nonlinear pulses

The dynamical behavior of a Holling II predator-prey model with control measures as nonlinear pulses is proposed and analyzed theoretically and numerically to understand how resource limitation affects pest population outbreaks. The threshold conditions for the stability of the pest-free periodic solution are given. Latin hypercube sampling/partial rank correlation coefficients are used to perform sensitivity analysis for the threshold concerning pest extinction to determine the significance of each parameter. Comparing this threshold value with that without resource limitation, our results indicate that it is essential to increase the pesticide’s efficacy against the pest and reduce its effectiveness against the natural enemy, while enhancing the efficiency of the natural enemies. Once the threshold value exceeds a critical level, both pest and its natural enemies populations can oscillate periodically. Furthermore,when the pulse period and constant stocking number as a bifurcation parameter, the predator-prey model reveals complex dynamics. In addition, numerical results are presented to illustrate the feasibility of our main results

Numerical Analysis of Discrete Switching Prey-Predator Model for Integrated Pest Management

The switching discrete prey-predator model concerning integrated pest management has been proposed, and the switches are guided by the economic threshold (ET). To begin with, the regular and virtual equilibria of switching system have been discussed and the key parameter bifurcation diagrams for the existence of equilibria have been proposed, which reveal the three different regions of equilibria. Besides, numerical bifurcation analyses show that the switching discrete system may have complicated dynamics behavior including chaos and the coexistence of multiple attractors. Finally, the effects of key parameters on the switching frequencies and switching times are discussed and the sensitivity analysis of varying parameter values for mean switching times has also been given. The results proved that economic threshold (ET) and the growth rate (α) were the key parameters for pest control

Comparison of predator-parasitoid-prey interaction models for different host plant qualities

Population dynamics models suggest that the over-all level of resource productivity plays an important role in community dynamics. One such factor of resource productivity is the quality of the host plant, which can determine the effectiveness of entomophagous (predatory and parasitoid) species by altering the growth rate of the phytophagous population via effects on fecundity, survival, and rate of development. These effects have been studied in relation to the distribution of host plants and their physiological state. However, few studies have considered the differences among plant cultivars. The objective of this study was to identify a continuous-time dynamic model, to describe the effects of different tomato cultivars on a one predatortwo prey model. The experiment was carried out under greenhouse conditions using ten tomato cultivars, with the predatory species Nesidiocoris tenuis (Reuter) (Insecta, Hemiptera, Miridae) and two prey species: the phytophagous species Bemisia tabaci (Gennadius) (Insecta, Hemiptera, Aleyrodidae) and the parasitoid species Trichogramma achaeae (Nagaraja & Nagarkatti) (Insecta, Hymenoptera, Trichogrammatidae); the latter was used as the intraguild-prey. Using the software SIMFIT, we found that a three-dimensional Lotka-Volterra type system could be well fitted to the data, estimating the phytophagous species´ growth rate, the parasitoid and predator mortality rates, the predation and parasitism rates, and the parasitoid emergence rate according to the cultivar type. The results showed an important effect of the host plant quality, by cultivar, on intraguild predation, resulting in important changes in the dynamics of phytophagous populations. These results are also discussed in relation to their importance in the biological control of pest species in greenhouse crops

AN INTRASEASONAL BIOECONOMIC MODEL OF PLRV NET NECROSIS

A bioeconomic model is developed as an IPM planning tool to combat PLRV net necrosis in the PNW potato industry. Environmental/biological and production processes are linked to marketing activities using discrete time control. We find that pesticides can be optimally timed to reduce applications and still protect against net necrosis.Crop Production/Industries, Environmental Economics and Policy,

The Optimal Release of Sterile Males in Pest Management

With an application of the sterile insect technique, it is our goal to know the optimal rate of production of sterile males in order to control an insect pest invasion and protect crops. Starting with a fundametal relationship between costs of production and feeding rates, we construct an objective functional. We then use the relationships between the dierent stages of female reproduction to build the state equations. Once, we have dened the optimal control problem, we use the simulated annealing algorithm to determine the amount of sterile males to be released at each discrete time event. Multiple calculations are made with dierent release schedules

Dynamics of a Double-Impulsive Control Model of Integrated Pest Management Using Perturbation Methods and Floquet Theory

We formulate an integrated pest management model to control natural pests of the crop through the periodic application of biopesticide and chemical pesticides. In a theoretical analysis of the system pest eradication, a periodic solution is found and established. All the system variables are proved to be bounded. Our main goal is then to ensure that pesticides are optimized, in terms of pesticide concentration and pesticide application frequency, and that the optimum combination of pesticides is found to provide the most benefit to the crop. By using Floquet theory and the small amplitude perturbation method, we prove that the pest eradication periodic solution is locally and globally stable. The acquired results establish a threshold time limit for the impulsive release of various controls as well as some valid theoretical conclusions for effective pest management. Furthermore, after a numerical comparison, we conclude that integrated pest management is more effective than single biological or chemical controls. Finally, we illustrate the analytical results through numerical simulations.Comment: This is a preprint of a paper whose final and definite form is published Open Access in 'Axioms' at [https://doi.org/10.3390/axioms12040391

Pareto-efficient biological pest control enable high efficacy at small costs

Biological pest control is increasingly used in agriculture as a an alternative to traditional chemical pest control. In many cases, this involves a one-off or periodic release of entomopathogens. As the interaction between the entomopathogen and the pest is complex and the production of entomopathogens potentially expensive, it is not surprising that both the efficacy and economic viability of biological pest control are debated. Here, we investigate the performance of very simple control strategies. In particular, we show how Pareto-efficient one-off or periodic release strategies, which optimally trade off between efficacy and economic viability, can be devised and used to enable high efficacy for small economic costs. We demonstrate our method on a pest-pathogen-crop model with a tunable immigration rate of pests. By analyzing this model, we demonstrate that simple Pareto-efficient one-off release strategies are typically efficacious and simultaneously have average profits that are close to the theoretical maximum obtained by less efficacious and complicated profit-optimizing strategies. The only exception occurs for high pest-immigration rates, in which case periodic release is preferable. The methods presented here can be extended to more complex scenarios and thus be used to identify promising biological pest control strategies in many circumstances