Stochastic plant–herbivore interaction model with Allee effect

Asfaw, Manalebish Debalike; Kassa, Semu Mitiku; Lungu, Edward M.

doi:10.1007/s00285-019-01425-5

Cited by 7 publications

(10 citation statements)

References 15 publications

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“…Based on the characteristics of plant diseases transmitted by insect vectors [7,8], we proposed the mathematical models with continuous control strategy and pulse control strategy with single-pulse sequence of multipulse sequences, developed the corresponding threshold theoretical analysis and numerical techniques to address the threshold dynamics of the model, and obtained the corresponding threshold conditions [10].…”

Section: Discussionmentioning

confidence: 99%

“…Plant diseases are caused by plant viruses transmitted by insect vectors [1][2][3][4][5], which can cause serious losses in economy and increased poverty [6]. Moreover, vector activity and behavior, especially in relation to virus transmission, are key to determining severity of plant disease transmission [7][8][9][10][11][12][13]. erefore, the development of corresponding prevention and control strategies of plant infectious diseases plays a very important role in protecting plants and eradicating vectors.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of a High-Dimensional Mathematical Model for Plant Virus Transmission with Continuous and Impulsive Roguing Control

Qiu

Tang

2021

Discrete Dynamics in Nature and Society

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Roguing and replanting are the most common strategies to control plant diseases and pests. How to build the mathematical models of plant virus transmission and consider the impact of roguing and replanting strategies on plant virus eradication is of great practical significance. In the present paper, we propose the mathematical models for plant virus transmission with continuous and impulsive roguing control. For the model with continuous control strategies, the threshold values for the existences and stabilities of multiple equilibria have been given, and the effect of roguing strategies on the threshold values is also addressed. Furthermore, the model with impulsive roguing control tactics is proposed, and the existence and stability of the plant-only and disease-free periodic solutions of the model are investigated by calculating several threshold values. Moreover, when selecting the design control strategy to minimize the threshold, we systematically analyze the existence of the optimal times of roguing infected plants within a replanting cycle, which is of great significance to the design and optimization of the prevention and control strategy of plant virus transmission. Finally, numerical investigations are given to reveal the main conclusions, and the biological implications of the main results are briefly discussed in the last section.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of a High-Dimensional Mathematical Model for Plant Virus Transmission with Continuous and Impulsive Roguing Control

Qiu

Tang

2021

Discrete Dynamics in Nature and Society

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“…Remark: The solution of the stochastic model ( 23) does not tend to any nearby steady state (see for example Asfaw et al [20]). The stability analysis in this study refers to quasi stability about a deterministic steady state x so that instead of considering individual paths of t x x − , we shall evaluate the expectation of…”

Section: Dynamics Of the Price: Stochastic Modelmentioning

confidence: 99%

Modeling Botswana Beef-Cattle Price Dynamics

Ziwakaya¹,

Lungu²

2021

JMF

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We investigate the dynamics of the beef-cattle pricing which is affected by several factors such as beef supply, demand for foreign currency, etc. The model incorporates mean-reversion to give insights into the relationship between supply to a developed region (or country) and a third world country's demand for hard currency. We consider the beef-cattle industry which is segmented into two markets: the Farmer-Local Cattle Agency (LCA) market in which the LCA buys cattle from the farmers and the LCA-European Union (EU) market in which the LCA exports beef to the EU. Using the Botswana-EU as an example, we investigate the performance of the Botswana Meat Commission (BMC) which buys cattle from the farmers and exports beef to the EU based on the price acceptable to the EU and ask whether the agreed price between the BMC and the EU can ever translate into fair price between the farmer and the BMC. Our study has concluded that the operational problems faced by the BMC are an indication that the BMC is passing on the bulk of what it receives from the EU to the farmers. We have made suggestions on how the BMC can reduce its operational risks.

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“…Lin et al [23] investigated the dynamical behaviors of a predator-prey model with non-monotonic functional response type and weak Allee effects on the prey. Asfaw et al [24] considered a stochastic extension of a model. They reported that noise adding to the plant population caused less change in the dynamics than noise adding to the herbivore population.…”

Section: Introductionmentioning

confidence: 99%

Impact of delay parameter on plant-herbivore dynamics under allee effect

Kumar

Verma

2022

J. Phys.: Conf. Ser.

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In this paper, plant-herbivore dynamics have been studied under the Allee effect using delay differential equations. The state variables considered are: plant population and herbivores. The boundedness and positivity of solutions are established. The interior equilibrium point is calculated for both, strong and weak Allee effect. It is shown that both the populations-plant and herbivores perish under the strong Allee effect. The stability of the system around the interior equilibrium under weak Allee effect is checked. Hopf-Bifurcation occurred at the critical value of the delay parameter. Numerical results have been supported graphically using MATLAB.

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Stochastic plant–herbivore interaction model with Allee effect

Cited by 7 publications

References 15 publications

Analysis of a High-Dimensional Mathematical Model for Plant Virus Transmission with Continuous and Impulsive Roguing Control

Analysis of a High-Dimensional Mathematical Model for Plant Virus Transmission with Continuous and Impulsive Roguing Control

Modeling Botswana Beef-Cattle Price Dynamics

Impact of delay parameter on plant-herbivore dynamics under allee effect

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