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

Jatav, Kunwer Singh; Dhar, Joydip; Nagar, Atulya K.

doi:10.1016/j.amc.2014.04.029

Cited by 4 publications

(3 citation statements)

References 28 publications

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“…Now the common pest control strategies include chemical control (spraying pesticides) and biological control (releasing natural enemies). Many scholars [1][2][3][4][5][6][7][8][9][10] used mathematical models to simulate pest control strategies. Some of them [1][2][3][4] analyzed the dynamics of the pest control models based on biological control.…”

Section: Introductionmentioning

confidence: 99%

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A pest control model with birth pulse and residual and delay effects of pesticides

Huang

Liu

2019

Adv Differ Equ

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Pesticides often cause residual and delayed effects on pests. Considering these effects, we use a pollution emission model to simulate the process of spraying pesticides. Many pests reproduce only at a fixed time in a year. So a pest control model with birth pulse and spraying pesticides is proposed. Using the limit system of the developed model, we analyze the dynamics of the system. The stability of the trivial equilibrium and the positive equilibrium of the model is analyzed, and the threshold conditions of pest eradication and permanence of the system are given. We obtain the optimal frequency of spraying pesticides by numerical simulations. The important parameters related to the pest eradication or permanence of the system are given by analyzing the sensitivity of the parameters. Finally, biological explanations are provided.

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Section: Introductionmentioning

confidence: 99%

“…Many scholars [1][2][3][4][5][6][7][8][9][10] used mathematical models to simulate pest control strategies. Some of them [1][2][3][4] analyzed the dynamics of the pest control models based on biological control. Whereas some studies [5][6][7][8][9][10] built pest management models only based on chemical controls.…”

Section: Introductionmentioning

confidence: 99%

A pest control model with birth pulse and residual and delay effects of pesticides

Huang

Liu

2019

Adv Differ Equ

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“…Reference mosquito specimens have been stored in Entomology Division, Defence Research and Development Establishment, Gwalior. Keeping in view of the compartmental modelling approaches [6,7,13,14,15], in this paper, an attempt is made to develop a mathematical model from field data for mosquito population considering all the stage via aquatic and adult stage.…”

Section: Introductionmentioning

confidence: 99%

Mathematical modelling and estimation of seasonal variation of mosquito population: a real case study

Dhar

Chaudhary

Baghel³

et al. 2014

bspm

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A mathematical model is proposed and analyzed for the understanding of growth pattern of mosquito vector looking into its life cycle. The objective of this study is to develop a mathematical model that can fit to the real data provided by DRDE scientist for different month at different stations so that the seasonal variation in population density of mosquitoes can be reported accurately to the estimated data obtained by the proposed mathematical model. The aquatic class (L) and adult stage is divided in two class, indoor population (I) and outdoor population (O). Here we estimated different parameters of our proposed continuous model and numerical simulation is done to compare the estimated data with the actual data.

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Controlling Pest by Integrated Pest Management: A Dynamical Approach

Kumari¹,

Chauhan²,

Dhar³

2020

Int J Math, Eng, Manag Sci

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Integrated Pest Management technique is used to formulate a mathematical model by using biological and chemical control impulsively. The uniform boundedness and the existence of pest extinction and nontrivial equilibrium points is discussed. Further, local stability of pest extinction equilibrium point is studied and it has been derived that if T≤T_max, the pest extinction equilibrium point is locally stable and for T>T_max, the system is permanent. It has also been obtained that how delay helps in eradicating pest population more quickly. Finally, analytic results have been validated numerically.

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

Cited by 4 publications

References 28 publications

A pest control model with birth pulse and residual and delay effects of pesticides

A pest control model with birth pulse and residual and delay effects of pesticides

Mathematical modelling and estimation of seasonal variation of mosquito population: a real case study

Controlling Pest by Integrated Pest Management: A Dynamical Approach

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