Effect of Fear, Treatment, and Hunting Cooperation on an Eco-Epidemiological Model: Memory Effect in Terms of Fractional Derivative

Ghosh, Uttam; Thirthar, Ashraf Adnan; Mondal, Bapin; Majumdar, Prahlad

doi:10.1007/s40995-022-01371-w

Cited by 12 publications

(17 citation statements)

References 50 publications

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“…There have been numerous studies in the field that have documented the presence of parasite infection in both prey and predators. Parasites can hinder the survival and reproductive capacity of infected organisms by disrupting their internal mechanisms [32]. Data obtained from field surveys and experimental studies on terrestrial vertebrates indicate that fear of predation leads to significant variation in prey density [33].…”

Section: Introductionmentioning

confidence: 99%

Predator–Prey Interaction with Fear Effects: Stability, Bifurcation and Two-Parameter Analysis Incorporating Complex and Fractal Behavior

Din,

Naseem,

Shabbir

2024

Fractal Fract

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This study investigates the dynamics of predator–prey interactions with non-overlapping generations under the influence of fear effects, a crucial factor in ecological research. We propose a novel discrete-time model that addresses limitations of previous models by explicitly incorporating fear. Our primary question is: How does fear influence the stability of predator–prey populations and the potential for chaotic dynamics? We analyze the model to identify biologically relevant equilibria (fixed points) and determine the conditions for their stability. Bifurcation analysis reveals how changes in fear levels and predation rates can lead to population crashes (transcritical bifurcation) and complex population fluctuations (period-doubling and Neimark–Sacker bifurcations). Furthermore, we explore the potential for controlling chaotic behavior using established methods. Finally, two-parameter analysis employing Lyapunov exponents, spectrum, and Kaplan–Yorke dimension quantifies the chaotic dynamics of the proposed system across a range of fear and predation levels. Numerical simulations support the theoretical findings. This study offers valuable insights into the impact of fear on predator–prey dynamics and paves the way for further exploration of chaos control in ecological models.

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Section: Introductionmentioning

confidence: 99%

Predator–Prey Interaction with Fear Effects: Stability, Bifurcation and Two-Parameter Analysis Incorporating Complex and Fractal Behavior

Din,

Naseem,

Shabbir

2024

Fractal Fract

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“…In the last few years, many prey-predator mathematical models have been developed to investigate the consequences of fear effect. In [9][10][11][12] ecological models with fear effect are investigated, while, fear effect in eco-epidemiological models are thoughtful in [13][14][15][16][17]. Various biological deductions have been reached based on the different assumptions included in these mathematical models.…”

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confidence: 99%

“…Through the use of mathematical, ecological, and eco-epidemiological models, lots of studies have been investigated the implications of intra-species cooperation. For instance, cooperative hunting can change how predator-prey models behave, and may resulting in intricate patterns with several periodic cycles [15][16][17][23][24][25][26]. So, including the function of cooperation in ecological and eco-epidemiological systems is essential to study and analysis species interactions and population dynamics.…”

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confidence: 99%

“…In last years, some research papers have proposed models that explore the dynamics between preys and predators, specifically focusing on the presence of diseases within prey species. These studies have also investigated the impact of fear on the growth of susceptible prey and its role in reducing interactions between susceptible and infected individuals [13][14][15][16][17]. While authors in [14,15,17] assume the predator eating both healthy and ill preys, and hence they used the cost of fear on the healthy preys growth and their contact with ill preys.…”

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confidence: 99%

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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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“…where, ϕ i (t) ≥ 0 with −T ≤ t ≤ 0 for i = 1, 2, 3, and the biological interpretation of all parameters describes in Table 1. Death rate of susceptible predator 0.5 [44,9] 3. Some basic results.…”

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confidence: 99%

A brief discussion about a predator-prey model including disease in predators with the delay effect

Das,

Chakraborty

2023

NACO

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Prey-predator interactions in an ecosystem are greatly influenced by the gestation delay and disease. To analyze the complex dynamics of the prey-predator interaction, we have proposed a three-tire delayed eco-epidemic model including disease in the predator population. During the study of this model, we establish the positivity and boundedness of the proposed model and also find all possible equilibrium points with their local and global stability condition in absence and presence of gestation delay. Analytical and numerical studies explain the existence of Transcritical and Hopf-bifurcations. Using sensitivity analysis, we examine the positive and negative impact of all model parameters and identify the most significant parameters. The main objective is to understand how disease and gestation delay influence the populations of this proposed model and also examine the combined effect of both gestation delay and disease infection rate. Furthermore, we incorporate the disease transmission delay and explore the combined effect of both gestation delay and disease transmission delay on the solutions of the proposed system. Numerically, we have demonstrated that the system experiences only steady and periodic behavior under the influence of gestation delay, but under the combined impact of both gestation delay and disease transmission delay, the system undergoes stable, one-periodic, two-periodic, and chaotic regimes.

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Effect of Fear, Treatment, and Hunting Cooperation on an Eco-Epidemiological Model: Memory Effect in Terms of Fractional Derivative

Cited by 12 publications

References 50 publications

Predator–Prey Interaction with Fear Effects: Stability, Bifurcation and Two-Parameter Analysis Incorporating Complex and Fractal Behavior

Predator–Prey Interaction with Fear Effects: Stability, Bifurcation and Two-Parameter Analysis Incorporating Complex and Fractal Behavior

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

A brief discussion about a predator-prey model including disease in predators with the delay effect

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