Pest-extinction Periodic Solution Research Articles

Effects of additional food availability and pulse control on the dynamics of a Holling-($ p $+1) type pest-natural enemy model

<abstract><p>In this paper, a novel pest-natural enemy model with additional food source and Holling-($ p $+1) type functional response is put forward for plant pest management by considering multiple food sources for predators. The dynamical properties of the model are investigated, including existence and local asymptotic stability of equilibria, as well as the existence of limit cycles. The inhibition of natural enemy on pest dispersal and the impact of additional food sources on system dynamics are elucidated. In view of the fact that the inhibitory effect of the natural enemy on pest dispersal is slow and in general deviated from the expected target, an integrated pest management model is established by regularly releasing natural enemies and spraying insecticide to improve the control effect. The influence of the control period on the global stability and system persistence of the pest extinction periodic solution is discussed. It is shown that there exists a time threshold, and as long as the control period does not exceed that threshold, pests can be completely eliminated. When the control period exceeds that threshold, the system can bifurcate the supercritical coexistence periodic solution from the pest extinction one. To illustrate the main results and verify the effectiveness of the control method, numerical simulations are implemented in MATLAB programs. This study not only enriched the related content of population dynamics, but also provided certain reference for the management of plant pest.</p></abstract>

An Integrated Eco-Epidemiological Plant Pest Natural Enemy Differential Equation Model with Various Impulsive Strategies

We established a mathematical model based on the sense of biological survey in the field of agriculture and introduced various control methods on how to prevent the crops from destructive pests. Basically, there are two main stages in the life cycle of natural enemies like insects: mature and immature. Here, we construct a food chain model of plant pest natural enemy. In natural enemies, there are two stages of construction. Also, we consider three classes of diseases in the pest population, namely, susceptible, exposed, and infectious in this proposed work. In order to categorize the considered models into the class of Impulsive Differential Equations (IDEs), in our study, we specifically consider two ecosystems, which define the impact of control mechanisms on the impulsive releasing of virus particle natural enemies and infectious pests at particular time. Additionally, the importance of spraying virus particles in pest control is discussed; then, we obtain two types of periodic solutions for the system, namely, plant pest extinction and pest extinction. By utilizing the small amplitude perturbation techniques and Floquet theory of the impulsive equation, we obtain the local stability of both periodic solutions. Moreover, the comparison technique of IDE shows the sufficient conditions for the global attractivity of a pest extinction periodic solution. With the assistance of the comparison results, we draw a numerical calculation for the addressed models. Finally, we extend the study of the two models for pest management models: with and without the existence of virus particle.

Stability Analysis of Integrated Pest Management with Impulsive Biological Control

The aim of the present work is to study the dynamics of stage-structured pest control model including biological control, i.e. by releasing of natural enemies and infected pests periodically. It is assumed that only immature susceptible pests are attacked by natural enemies admitting Beddington DeAngelis functional response and mature susceptible pests are contacted by infected pests with bilinear incidence rate and become exposed. The sufficient condition for local stability of pest extinction periodic solution is derived by making use of Floquet’s theory and small amplitude perturbation technique. The global attractivity of pest extinction periodic solution is also established by applying comparison principle of impulsive differential equations.

Dynamics Properties of a Delayed Stage-structure Predator-prey System with Biological Control Strategy

Based on the biological control strategy in the pest management, the dynamic properties of a ratio-dependent and delayed stage-structure predator-prey system with Holling type III functional response is investigated. The global attractivity of the pest-extinction periodic solution and the permanence of the system are studied by using the theories and methods of impulsive delayed differential equation. Numerical simulations are carried out to illustrate the main results.

Stability and permanence of an eco-epidemiological SEIN model with impulsive biological control

Natural enemies of insects are extremely important in preventing pest outbreaks in crop fields. Therefore, we investigate the dynamical behavior of a pest-dependent consumption pest–natural enemy (i.e., prey–predator) SEIN model concerning diseases in pest population with three classes (susceptible–exposed–infectious) and impulsive releasing of infectious pests and natural enemies at fixed moments of time. We prove that all solutions of the system are uniformly ultimately bounded. In first part of the main results, the sufficient conditions for local as well as global asymptotic stability of the susceptible and exposed pest extinction periodic solution are determined using a Floquet’s theorem of impulsive differential equations, small-amplitude perturbation skills and comparison theorem. In second part, the sufficient condition for the permanence of a system is determined. These dynamics imply that susceptible and exposed pest populations become extinct when impulse period is less than some critical value and pests coexist with natural enemies at low level when impulse period crosses the critical value. Thus, our results provide some reliable theoretical tactics for pest management and finally these are verified by performing some numerical simulations.

Mathematical study of stage-structured pests control through impulsively released natural enemies with discrete and distributed delays

Many insect pest species have two major stages in their life-history: an immature larval stage and a mature adult stage. The immature larval stage may have a significant duration, during which the insect may not be the same natural predators as in the adult stage. Keeping this biological background in mind, we propose a stage-structured natural enemy–pest model with distributed and discrete delays for natural enemy and pest, respectively. It is also assumed that the natural enemies are released in an impulsive manner. The global attractivity of the pest-extinction periodic solution of the system is obtained using comparison techniques on impulsive delay differential equations. Furthermore, the permanence conditions for the coexistence of the species are explored, which indicates that the maturation time delay and the amount of natural enemies released in a pulse can affect the dynamics of the system. The threshold values for maturation delay of pest and the releasing amount natural enemy are obtained for extinction and permanence of the species. Finally, numerical simulation is given in support of validation of the theoretical results to provide a strategic basis for the biological pest management.

Hybrid approach for pest control with impulsive releasing of natural enemies and chemical pesticides: A plant–pest–natural enemy model

The agricultural pests can be controlled effectively by simultaneous use (i.e., hybrid approach) of biological and chemical control methods. Also, many insect natural enemies have two major life stages, immature and mature. According to this biological background, in this paper, we propose a three tropic level plant–pest–natural enemy food chain model with stage structure in natural enemy. Moreover, impulsive releasing of natural enemies and harvesting of pests are also considered. We obtain that the system has two types of periodic solutions: plant–pest-extinction and pest-extinction using stroboscopic maps. The local stability for both periodic solutions is studied using the Floquet theory of the impulsive equation and small amplitude perturbation techniques. The sufficient conditions for the global attractivity of a pest-extinction periodic solution are determined by the comparison technique of impulsive differential equations. We analyze that the global attractivity of a pest-extinction periodic solution and permanence of the system are evidenced by a threshold limit of an impulsive period depending on pulse releasing and harvesting amounts. Finally, numerical simulations are given in support of validation of the theoretical findings.

Dynamics on a pest management SI model with control strategies of different frequencies

Based on spraying pesticide and introducing infected pest and natural enemy for pest control, an SI ecological epidemic model with different frequencies of pesticide applications and infected pests and natural enemy releases is proposed and studied. With spraying either more or less frequently than the releases, the threshold condition of existence and global attractiveness of susceptible pest extinction periodic solution is obtained. We investigate the effects of the pest control tactics on the threshold conditions. We also show that the system has rich dynamics including period-doubling bifurcations and chaos as the release period increases, which implies that the presence of impulsive intervention makes the dynamic behavior more complex. Finally, to see how the pesticide applications can be reduced, we develop a model involving periodic releases of natural enemies with chemical control applied only when the densities of the pest reaches the given Economic Threshold. It indicates that the hybrid method is the most effective method to control pest and the frequency of pesticide applications largely depends on the initial densities and the control tactics.

The Study of a Class of Pest Control Pollution Model with Stage-Structure and Time Delay

We construct a pest control pollution model with stage-structure for pests and with epidemic in the predator by spraying pesticides and releasing susceptible predators together. We assume that only the pests and infective predators are affected by pesticide. We show that there exists a globally attractive pest-extinction periodic solution and we get the condition of global attractiveness of the pest-extinction periodic solution by applying comparison theorem of impulsive differential equation. Further, the condition for the permanence of the system is also given.

Analysis of pest-epidemic model by releasing diseased pest with impulsive transmission

According to biological and chemical control strategy for pest control, we investigate an SI model for pest management, concerning periodic spraying of microbial pesticide and releasing infected pests at different fixed moments. By using Floquet and comparison theorems, we prove that the pest-extinction periodic solution is globally asymptotically stable when the impulsive period T is less than the critical value Tmax . Otherwise, the system can be permanent. Our results provide reliable tactic basis for the practical pest management.

The dynamics of pest control pollution model with age structure and time delay

In this paper, by using pollution model and impulsive delay differential equation, we investigate the dynamics of a pest control model with age structure for pest by introducing a constant periodic pesticide input and releasing natural enemies at different fixed moment. We assume only the pests are affected by pesticide. We show that there exists a global attractive pest-extinction periodic solution when the periodic natural enemies release amount μ 1 and pesticide input amount μ 2 are larger than some critical value. Further, the condition for the permanence of the system is also given. By numerical analyses, we also show that constant maturation time delay, pulse pesticide input and pulse releasing of the natural enemies can bring obvious effects on the dynamics of system. We believe that the results will provide reliable tactic basis for the practical pest management.

Modelling and Analysis of a Pest-Control Pollution Model with Integrated Control Tactics

A hybrid impulsive pest control model with stage structure for pest and Holling II functional response is proposed and investigated, in which the effects of impulsive pesticide input in the environment and in the organism are considered. Sufficient conditions for global attractiveness of the pest-extinction periodic solution and permanence of the system are obtained, which show that there exists a globally asymptotically stable pest-extinction periodic solution when the number of natural enemies released is more than some critical value, whereas the system can be permanent when the number of natural enemies released is less than another critical value. Furthermore, numerical simulations are carried out to illustrate our theoretical results and facilitate their interpretation.

A Pest Management Epidemic Model with Time Delay and Stage-Structure

In this paper, an SI epidemic model with stage structure is investigated. In this model, impulsive biological control which release infected pest to the field at a fixed time periodically is considered, and obtained the sufficient conditions for the global attractivity of pest-extinction periodic solution and permanence of the system. We also prove that all solutions of the model are uniformly ultimately bounded. The sensitive analysis on the two thresholds and to the changes of the releasing amounts of infected pest is shown by numerical simulations. Our results provide a reliable tactic basis for the practice of pest management.

Mathematical model for the control of a pest population with impulsive perturbations on diseased pest

In this paper, a stage-structured pest management SI model with impulsive perturbations on infected pest is introduced. Sufficient conditions of the global attractivity of pest-extinction periodic solution and permanence of the system are obtained. We also prove that all solutions of system are uniformly ultimately bounded.

A Mutual Interference Stage-Structured Predator-Prey Model with Time Delay and Impulsive Perturbations on Predators

A mutual interference stage-structured predator-prey model is considered with time delay and impulsive perturbation on predators.Sufficient conditions are obtained,which guarantee the global attractivity of pest-extinction periodic solution and permanence of the system.It is shown that all solutions of the system are uniformly ultimately bounded.The obtained results can be helpful for the practical pest management.

Impulsive control strategy of a pest management SI model with nonlinear incidence rate

In this work, we consider a pest management SI model with impulsive release of infective pests and spraying pesticides. We prove that all solutions of the investigated system are uniformly ultimately bounded and the pest-extinction periodic solution is globally asymptotically stable when some condition is satisfied. We also obtain the permanent condition of the system. It is concluded that the approach of combining impulsive release of infective pests with impulsive spraying pesticides provides reliable tactic basis for the practical pest management.

GLOBAL ATTRACTIVITY AND PERMANENCE OF A STAGE-STRUCTURED PEST MANAGEMENT SI MODEL WITH TIME DELAY AND DISEASED PESTS IMPULSIVE TRANSMISSION

In this work, we consider a stage-structured pest management SI model with time delay and diseased pests impulsive transmission. Sufficient conditions which guarantee the global attractivity of pest-extinction periodic solution and permanence of the system are obtained. We also prove that all solutions of the system are uniformly ultimately bounded. Our results provide reliable tactic basis for the practical pest management.

A stage-structured Holling mass defence predator–prey model with impulsive perturbations on predators

In this work, we consider a stage-structured Holling mass defence predator–prey model with time delay and impulsive transmitting on predators. Sufficient conditions which guarantee the global attractivity of pest-extinction periodic solution and permanence of the system are obtained. We also prove that all solutions of the system are uniformly ultimately bounded. Our results provide reliable tactic basis for the practical pest management.