The Dynamical Analysis of a Delayed Prey-Predator Model with a Refuge-Stage Structure Prey Population

Naji, Raid Kamel; Majeed, Salam J.

doi:10.29252/ijmsi.15.1.135

Cited by 5 publications

(3 citation statements)

References 24 publications

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“…Figures (1)(2) show that the infection force parameter 𝛼 has an extinction effect on the infected prey and predator species. Figures (3)(4) show that the infected prey refuge parameter 𝜃 has the same effect on the predator species. Finally, as shown in Figure (5)(6), fear level rate 𝑘 2 has a beneficial effect on the overall coexistence of the system since it is an instability effect at the start, but when it exceeds a certain level, it has a stability effect and the system switches for cyclic dynamic to stable oscillations and then to stable steady state.…”

Section: -Conclusionmentioning

confidence: 93%

Bifurcation Analysis of an eco-epidemiological model involving prey refuge, fear impact and hunting cooperation

Alaa khadim Mohammed1,

Salam Jasim Majeed

2024

JEPS

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This paper centers on an eco-epidemiological predator-prey model that accounts for hunting cooperation among predators and prey shelter and fear in afflicted prey. The objective is to investigate the effects of parameter factors on the model's bifurcation behavior. Theoretical part of this study demonstrate that a transcritical bifurcation can result from infection rate and refuge rate. Furthermore, fear rate can cause a Hopf-bifurcation to arise close to the positive equilibrium point. The presence of local bifurcations close to the non-trivial equilibrium points is verified by numerical analysis, which also guarantees the veracity of the theoretical results.

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Section: -Conclusionmentioning

confidence: 93%

Bifurcation Analysis of an eco-epidemiological model involving prey refuge, fear impact and hunting cooperation

Alaa khadim Mohammed1,

Salam Jasim Majeed

2024

JEPS

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“…The basic reproduction number [17] infected tea can produce more than one secondary infection [18][19][20][21]. In this case, the disease-free equilibrium is unstable so that it can cause the epidemic outbreaks.…”

Section: Basic Reproduction Numbermentioning

confidence: 99%

Stability Analysis of Dynamical Model Interactions Tea Plants, Pests, and Diseases With Fungicides and Insecticides Controls

Diana

Widowati

Tjahjana

et al. 2023

ijmcr

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Tea plants are one of the exports commodities in Indonesia. In their development, the plantation ecosystem is heavily influenced by several factors, both internal and external factors. In the field of applied mathematics, mathematical modelling can be used to analyze the development of tea plant growth and their interactions each other in their ecosystem. The mathematical model in this research is combining three main models, there are logistic model, epidemiological model, and predator prey model by adding fungicide and insecticide controls. Furthermore, local and global stability analysis is carried out and the optimal control problem is solved by Pontryagin maximum principle. The results of the analysis obtained five equilibrium points. Local stability analysis was carried out using the Routh Hurwitz criteria which showed the fifth equilibrium point is locally asymptotically stable. The basic reproduction number in the model is 0.99. Because 16R0<1" style="width: 28pt; height: 11pt;">, it can be concluded that there is no spread of disease in the tea plantation ecosystem after a period of 5 years. The control provided can reduce pest and disease attacks. After being given control, the population of infected tea plants decreased by 93.21%, Empoasca pests decreased by 99.47%, and leaf roller caterpillars decreased by 99.31% compared to the model that was not given control.

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“…[14] studied a delayed of SEIR epidemic model in which the latent and infected states are infective. Naji and Majeed [15] investigated the impact of delay on a stage-structure prey-predator model. Zhe Yin at el.…”

Section: Introductionmentioning

confidence: 99%

A robust Study of the Treatment Delay Effect on the Dynamics of Epidemic Disease

Ali,

Al-Husseiny

2024

Iraqi Journal of Science

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A general treatment function with an epidemic model that involves the delay in the treatment period has been proposed and studied in this work. This model contains two compartments, namely susceptible denoted by and infected denoted by . The existence of all the fixed points has been determined. The system has two equilibrium points, namely the uninfected equilibrium point (UIEP) and the endemic equilibrium point (EEP). The conditions for local stability and Hopf bifurcation have been discussed. The stability of the periodic solutions and the direction of the Hopf bifurcation properties have been studied analytically and numerically.

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The Dynamical Analysis of a Delayed Prey-Predator Model with a Refuge-Stage Structure Prey Population

Cited by 5 publications

References 24 publications

Bifurcation Analysis of an eco-epidemiological model involving prey refuge, fear impact and hunting cooperation

Bifurcation Analysis of an eco-epidemiological model involving prey refuge, fear impact and hunting cooperation

Stability Analysis of Dynamical Model Interactions Tea Plants, Pests, and Diseases With Fungicides and Insecticides Controls

A robust Study of the Treatment Delay Effect on the Dynamics of Epidemic Disease

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