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

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Jianwen Jia ◽  
Bo Wu
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Time Delay ◽  
Comparison Theorem ◽  
Pest Control ◽  
Impulsive Differential Equation ◽  
Stage Structure ◽  
Globally Attractive

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.

scholarly journals Dynamics of a Stage Structure Pest Control Model with Impulsive Effects at Different Fixed Time

2009 ◽  
Vol 2009 ◽  
pp. 1-15 ◽  
Author(s):  
Bing Liu ◽  
Ying Duan ◽  
Yinghui Gao
Keyword(s):  
Time Delay ◽  
Pest Control ◽  
Natural Enemies ◽  
Stage Structure ◽  
Threshold Level ◽  
Fixed Time ◽  
Control Model ◽  
Pest Population ◽  
Maturation Time ◽  
Maturation Time Delay

Many existing pest control models, which control pests by releasing natural enemies, neglect the effect that natural enemies may get killed. From this point of view, we formulate a pest control model with stage structure for the pest with constant maturation time delay (through-stage time delay) and periodic releasing natural enemies and natural enemies killed at different fixed time and perform a systematic mathematical and ecological study. By using the comparison theorem and analysis method, we obtain the conditions for the global attractivity of the pest-eradication periodic solution and permanence of the system. We also present a pest management strategy in which the pest population is kept under the economic threshold level (ETL) when the pest population is uniformly permanent. We show that maturation time delay, impulsive releasing, and killing natural enemies can bring great effects on the dynamics of the system. Numerical simulations confirm our theoretical results.

scholarly journals Global dynamics of a stage-structured hantavirus infection model with seasonality

2021 ◽  
Vol 26 (1) ◽  
pp. 21-40
Author(s):  
Junli Liu ◽  
Tailei Zhang
Keyword(s):  
Periodic Solution ◽  
Control Strategies ◽  
Stage Structure ◽  
Positive Periodic Solution ◽  
Clethrionomys Glareolus ◽  
Hantavirus Infection ◽  
Infection Model ◽  
Global Dynamics ◽  
Periodic Model ◽  
Globally Attractive

In this paper, we study a time-periodic model, which incorporates seasonality and host stage-structure. This model describes the propagation of Puumala hantavirus within the bank vole population of Clethrionomys glareolus. The basic reproduction number R0 is obtained. By appealing to the theory of monotone dynamical systems and chain transitive sets, we establish a threshold-type result on the global dynamics in terms of R0, that is, the virus-free periodic solution is globally attractive, and the virus dies out if R0 ≤ 1, while there exists a unique positive periodic solution, which is globally attractive, and the virus persists if R0 > 1. Numerical simulations are given to confirm our theoretical results and to show that cleaning environment and controlling the grow of mice population are essential control strategies to reduce hantavirus infection.

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

2010 ◽  
Vol 2010 ◽  
pp. 1-21 ◽  
Author(s):  
Yiping Chen ◽  
Zhijun Liu ◽  
Wenjie Qin
Keyword(s):  
Periodic Solution ◽  
Pest Control ◽  
Natural Enemies ◽  
Integrated Control ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Critical Value ◽  
Globally Asymptotically Stable ◽  
Holling Ii Functional Response ◽  
Theoretical Results

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.

Research on Impulsive Lurie Systems with Time-Delay

2014 ◽  
Vol 889-890 ◽  
pp. 633-636
Author(s):  
Xue Jun Li
Keyword(s):  
Differential Equation ◽  
Time Delay ◽  
Differential System ◽  
Stability Theory ◽  
Impulsive Differential Equation ◽  
Comparison Theory ◽  
Impulsive Differential System ◽  
Numerical Example ◽  
Impulsive Synchronization

Based on stability theory of impulsive differential equation and new comparison theory of impulsive differential system, some simple yet less conservative criteria ensuring impulsive synchronization of the Lurie systems are derived. A numerical example is given to illustrate the effectiveness of the method.

scholarly journals A Predator-Prey Gompertz Model with Time Delay and Impulsive Perturbations on the Prey

2009 ◽  
Vol 2009 ◽  
pp. 1-15 ◽  
Author(s):  
Jianwen Jia ◽  
Chunhua Li
Keyword(s):  
Dynamical System ◽  
Differential Equation ◽  
Time Delay ◽  
Impulsive Differential Equation ◽  
Global Attractivity ◽  
Discrete Dynamical System ◽  
Sufficient Conditions ◽  
Gompertz Model ◽  
Predator Prey ◽  
Impulsive Perturbations

We introduce and study a Gompertz model with time delay and impulsive perturbations on the prey. By using the discrete dynamical system determined by the stroboscopic map, we obtain the sufficient conditions for the existence and global attractivity of the “predator-extinction” periodic solution. With the theory on the delay functional and impulsive differential equation, we obtain the appropriate condition for the permanence of the system.

scholarly journals Multi-State Dependent Impulsive Control for Pest Management

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Huidong Cheng ◽  
Fang Wang ◽  
Tongqian Zhang
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Qualitative Analysis ◽  
Pest Management ◽  
Pest Control ◽  
Impulsive Control ◽  
Management Strategies ◽  
Control Methods ◽  
State Dependent ◽  
Order One Periodic Solution

According to the integrated pest management strategies, we propose a model for pest control which adopts different control methods at different thresholds. By using differential equation geometry theory and the method of successor functions, we prove the existence of order one periodic solution of such system, and further, the attractiveness of the order one periodic solution by sequence convergence rules and qualitative analysis. Numerical simulations are carried out to illustrate the feasibility of our main results. Our results show that our method used in this paper is more efficient and easier than the existing ones for proving the existence of order one periodic solution.

scholarly journals Stability Analysis of Hepatitis B Virus Model with Incomplete Immunization of HepB Vaccine

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Yan Cheng ◽  
Qiuhui Pan ◽  
Mingfeng He
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Fixed Point ◽  
Stability Analysis ◽  
Impulsive Differential Equation ◽  
Infection Model ◽  
B Virus ◽  
Virus Model ◽  
Impulsive Vaccination ◽  
Disease Free

In this paper a HBV infection model with impulsive vaccination is considered. By using fixed point theorem and stroboscopic map we prove the existence of disease-free T-periodic solution. Also by comparative theorem of impulsive differential equation we get the global asymptotic stability of the disease-free periodic solution and permanence of the disease. Numerical simulations show the influence of parameters on the dynamics of HBV, which provided references for seeking optimal measures to control the transmission of HBV.

scholarly journals Permanence, Extinction, and Almost Periodic Solution of a Nicholson's Blowflies Model with Feedback Control and Time Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Haihui Wu ◽  
Shengbin Yu
Keyword(s):  
Periodic Solution ◽  
Time Delay ◽  
Feedback Control ◽  
Control Variable ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Nicholson’S Blowflies Model ◽  
Positive Almost Periodic Solution ◽  
Globally Attractive

A Nicholson's blowflies model with feedback control and time delay is studied. By applying the comparison theorem of the differential equation and fluctuation lemma and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence, extinction, and existence of a unique globally attractive positive almost periodic solution of the system are obtained. It is proved that the feedback control variable and time delay have no influence on the permanence and extinction of the system.

scholarly journals Almost Periodic Solution of a Discrete Commensalism System

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Yalong Xue ◽  
Xiangdong Xie ◽  
Fengde Chen ◽  
Rongyu Han
Keyword(s):  
Periodic Solution ◽  
Comparison Theorem ◽  
Lyapunov Functional ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Discrete Lyapunov Functional ◽  
Globally Attractive

A nonautonomous discrete two-species Lotka-Volterra commensalism system with delays is considered in this paper. Based on the discrete comparison theorem, the permanence of the system is obtained. Then, by constructing a new discrete Lyapunov functional, a set of sufficient conditions which guarantee the system global attractivity are obtained. If the coefficients are almost periodic, there exists an almost periodic solution and the almost periodic solution is globally attractive.

Sign in / Sign up

Export Citation Format

Share Document