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

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.

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Bing Liu ◽  
Ling Xu ◽  
Baolin Kang

By using pollution model and impulsive delay differential equation, we formulate a pest control model with stage structure for natural enemy in a polluted environment by introducing a constant periodic pollutant input and killing pest at different fixed moments and investigate the dynamics of such a system. We assume only that the natural enemies are affected by pollution, and we choose the method to kill the pest without harming natural enemies. Sufficient conditions for global attractivity of the natural enemy-extinction periodic solution and permanence of the system are obtained. Numerical simulations are presented to confirm our theoretical results.


Author(s):  
Ayman A. Arafa ◽  
Soliman A.A. Hamdallah ◽  
Sanyi Tang ◽  
Yong Xu ◽  
Gamal M. Mahmoud

Insects ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 74
Author(s):  
Xiao-wei Li ◽  
Xin-xin Lu ◽  
Zhi-jun Zhang ◽  
Jun Huang ◽  
Jin-ming Zhang ◽  
...  

Intercropping of aromatic plants provides an environmentally benign route to reducing pest damage in agroecosystems. However, the effect of intercropping on natural enemies, another element which may be vital to the success of an integrated pest management approach, varies in different intercropping systems. Rosemary, Rosmarinus officinalis L. (Lamiaceae), has been reported to be repellent to many insect species. In this study, the impact of sweet pepper/rosemary intercropping on pest population suppression was evaluated under greenhouse conditions and the effect of rosemary intercropping on natural enemy population dynamics was investigated. The results showed that intercropping rosemary with sweet pepper significantly reduced the population densities of three major pest species on sweet pepper, Frankliniella intonsa, Myzus persicae, and Bemisia tabaci, but did not affect the population densities of their natural enemies, the predatory bug, Orius sauteri, or parasitoid, Encarsia formosa. Significant pest population suppression with no adverse effect on released natural enemy populations in the sweet pepper/rosemary intercropping system suggests this could be an approach for integrated pest management of greenhouse-cultivated sweet pepper. Our results highlight the potential of the integration of alternative pest control strategies to optimize sustainable pest control.


2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Yakui Xue ◽  
Xiafeng Duan

We invest a predator-prey model of Holling type-IV functional response with stage structure and double delays due to maturation time for both prey and predator. The dynamical behavior of the system is investigated from the point of view of stability switches aspects. We assume that the immature and mature individuals of each species are divided by a fixed age, and the mature predator only attacks the mature prey. Based on some comparison arguments, sharp threshold conditions which are both necessary and sufficient for the global stability of the equilibrium point of predator extinction are obtained. The most important outcome of this paper is that the variation of predator stage structure can affect the existence of the interior equilibrium point and drive the predator into extinction by changing the maturation (through-stage) time delay. Our linear stability work and numerical results show that if the resource is dynamic, as in nature, there is a window in maturation time delay parameters that generate sustainable oscillatory dynamics.


2013 ◽  
Vol 18 (4) ◽  
pp. 505-528 ◽  
Author(s):  
Tongqian Zhang ◽  
Xinzhu Meng ◽  
Yi Song ◽  
Tonghua Zhang

This paper aims to develop a high-dimensional SI model with stage structure for both the prey (pest) and the predator, and then to investigate the dynamics of it. The model can be used for the study of Integrated Pest Management (IPM) which is a combination of constant pulse releasing of animal enemies and diseased pests at two different fixed moments. Firstly, we use analytical techniques for impulsive delay differential equations to obtain the conditions for global attractivity of the ‘pest-free’ periodic solution and permanence of the population model. It shows that the conditions strongly depend on time delay, impulsive release of animal enemies and infective pests. Secondly, we present a pest management strategy in which the pest population is kept under the economic threshold level (ETL) when the pest population is permanent. Finally, numerical analysis is presented to illustrate our main conclusion.


2020 ◽  
Vol 14 (2) ◽  
pp. 72
Author(s):  
NURINDAH NURINDAH ◽  
DWI ADI SUNARTO

ABSTRAK<br />Helicoverpa armigera adalah salah satu hama utama pada kapas,<br />sehingga perlu dikendalikan. Konsep ambang kendali sebagai salah satu<br />komponen dalam PHT telah dikembangkan untuk H. armigera, namun<br />hanya berdasarkan populasi hama dan belum mempertimbangkan<br />keberadaan musuh alami. Penelitian ini bertujuan untuk menguji ambang<br />kendali H. armigera dengan mempertimbangkan keberadaan musuh alami<br />pada skala luas di daerah pengembangan dengan menggunakan lahan<br />petani. Penelitian ini dilakukan pada pertanaman kapas tumpangsari<br />dengan kedelai yang ditanam sesudah padi di Kecamatan Mantup dan<br />Kembangbau, Lamongan, Jawa Timur pada Maret-Oktober 2005. Lahan<br />yang digunakan seluas 15 hektar, di bawah pengelolaan 36 petani.<br />Pengujian ambang kendali H. armigera dilakukan dengan menerapkan dua<br />perlakuan konsep ambang kendali yang merupakan bagian dari PHT<br />kapas, yaitu: (1) AKH: 4 tanaman terinfestasi/25 tanaman contoh; dan (2)<br />AKH+MA: 4 tanaman terinfestasi/25 tanaman contoh; jumlah tanaman<br />yang terinfestasi yang teramati dikurangi 1 jika ditemukan 8 ekor predator<br />dan kelipatannya. Jika populasi pada petak perlakuan mencapai ambang<br />kendali, dilakukan penyemprotan dengan Ekstrak Biji Mimba (EBM).<br />Setiap lahan petani dibagi dua, setiap bagian menerapkan satu perlakuan<br />(n=36). Pengamatan dilakukan pada 25 unit pengamatan per 1,0 ha yang<br />diambil secara W sampling, setiap 7 hari sejak 50 hari setelah tanam (hst)<br />hingga 90 hst. Satu unit pengamatan adalah 1 m 2 . Parameter yang diamati<br />secara periodik adalah populasi H. armigera (telur dan larva); kerusakan<br />buah, hasil kapas berbiji, serta penggunaan saprodi dan tenaga kerja untuk<br />pengendalian hama. Data yang diperoleh dianalisa dengan menggunakan<br />uji t. Hasil penelitian menunjukkan bahwa populasi H. armigera pada<br />kapas + kedelai dapat ditekan oleh musuh alaminya, khususnya kompleks<br />predator yang terdiri atas laba-laba, kumbang kubah dan kepik mirid.<br />Populasi kompleks predator dapat mencapai 40-80 ekor/25 tanaman.<br />Dengan demikian, penerapan ambang kendali H. armigera pada kapas +<br />kedelai dengan memperhitungkan keberadaan predator menyebabkan tidak<br />perlu dilakukannya penyemprotan insektisida sama sekali, sehingga<br />terdapat keuntungan ekonomis, yaitu penghematan biaya saprodi sebesar<br />Rp 259.000 per hektar dan keuntungan ekologis, yaitu tidak tercemarnya<br />lingkungan oleh senyawa toksik.<br />Kata kunci : Kapas, Gossypium hirsutum L., ambang kendali, Helicoverpa<br />armigera, Jawa Timur<br />ABSTRACT<br />Action  threshold  for  Helicoverpa  armigera  by<br />considering the presence of predators on cotton<br />Helicoverpa armigera on cotton was considered as the main pest,<br />therefore it always be a focus of pest control. Action threshold concept as<br />an IPM component had been developed for H. armigera on cotton;<br />however it has not considered the presence of natural enemies. The<br />objective of this research is to test the action threshold of H. armigera by<br />considering the presence of natural enemies on cotton intercropped with<br />soybean in farmers’ fields. The test involved 15 hectares of farmers’<br />fields (involving 36 farmers) in Lamongan, East Java in March-October<br />2005. The action thresholds for H. armigera tested were: (1) AKH: 4<br />infested plants/25 sample plants; and (2) AKH+MA: 4 infested plants/25<br />sample plants, and the number of infested plants observed was subtracted<br />by 1 when 8 predators, and it’s folded up, were found in the sample plants.<br />Spray of neem seed extract (NSE) was applied when the pest population<br />reached action threshold level. Each farmer field was divided into two<br />parts to accommodate the treatments. The observations were made<br />periodically on 25 units per 1,0 hectare in 7-days interval on 50 – 90 days<br />after planting (dap). The size of observation unit was 1 m 2 . Parameters<br />observed included H. armigera population (egg and larva); damage bolls,<br />seed cotton production and the cost of pest control. Data were analysed by<br />using t-test. The results showed that H. armigera population on cotton<br />intercropped with soybean could be repress by its natural enemies,<br />especially by the complex predator (consisted of spiders, lady bird beetles<br />and predatory mirid bugs) to be always under action threshold level. The<br />application of action threshold by considering the presence of predator in<br />cotton + soybean fields would lead to unsprayed cultivation. Resulted<br />economical benefit by saving of the production cost Rp 259.000 per<br />hectare as well as ecological advantage by avoiding of sprays of toxic<br />materials in the environment.<br />Key words : Cotton,  Gossypium  hirsutum  L.,  action  threshold,<br />Helicoverpa armigera, East Java


2012 ◽  
Vol 538-541 ◽  
pp. 2522-2525
Author(s):  
Wen Cai Zhao ◽  
Tong Qian Zhang ◽  
Zheng Bo Chang

In this paper, on the basis of the theories and methods of ecology and ordinary differential equations, an ecological Gompertz model with Holling III functional response and stage structure for predator is established. By use of the stroboscopic map, a predator extinction periodic solution is obtained, and the global attractivity of the predator extinction periodic solution is analyzed. By using comparison theorem of impulsive differential equation and small amplitude perturbation skills, we get the sufficient condition for permanence of the system under impulsive harvest strategy for the prey and maturation time delay of predator.


2010 ◽  
Vol 2010 ◽  
pp. 1-21 ◽  
Author(s):  
Yiping Chen ◽  
Zhijun Liu ◽  
Wenjie Qin

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.


2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Samit Bhattacharyya ◽  
Suma Ghosh

We study the role of predation dynamics in oscillation of pest population in insect ecology. A two-dimensional pest control model (under the use of insecticides) with time delay in predation is considered in this paper. By the Hopf bifurcation theory, we prove the existence of the stable oscillation of the system. We also consider the economic viability of the control process. First we improve the Pontryagin maximum principle (PMP) where the delay in the system is sufficiently small and control function is linear, and then we apply the improved version of PMP to perform the optimal analysis of the pest control model as a special case.


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