Dynamic Analysis of a Heterogeneous Diffusive Prey-Predator System in Time-Periodic Environment

Dai, Chuanjun; He, Lixin; Jin, Zhan; Guo, Qing; Wang, Yi; Yu, Hengguo; Wang, Qi; Ma, Zengling; Zhao, Min

doi:10.1155/2020/7134869

Cited by 3 publications

(2 citation statements)

References 51 publications

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“…The Lotka-Volterra predator-prey model is essential for understanding the complex dynamics between FLA and bacteria. Originally, the formulation of the classic prey-predator model was introduced by Lotka (1925) and Volterra (1926), with Holling later extending these models, incorporating three functional responses for predation phenomena (Dai et al, 2020;Dennehy, 2020;Fumanelli et al, 2011;Holling, 1959;Lotka, 1925;Umar et al, 2019;Volterra, 1926).…”

Section: Simple Differential-equation-based Modelsmentioning

confidence: 99%

“…As spatial heterogeneity is pervasive in ecosystems, populations often experience variable conditions influenced by temporal fluctuations in temperature, light, and resource availability (Bernhardt et al, 2020). Furthermore, certain systems may exhibit seasonal dependencies as time‐periodic functions (Dai et al, 2020; Huang & Wang, 2019; Zhao et al, 2017). Therefore, employing mathematical models that account for spatial and temporal variability is essential for accurately representing these ecosystems.…”

Section: A Roadmap For Advancing Understanding Of Fla–bacteria Intera...mentioning

confidence: 99%

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Modelling dynamics between free‐living amoebae and bacteria

Ali,

Rice,

Byrne

et al. 2024

Environmental Microbiology

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Free‐living amoebae (FLA) serve as hosts for a variety of endosymbionts, which are microorganisms that reside and multiply within the FLA. Some of these endosymbionts pose a pathogenic threat to humans, animals, or both. The symbiotic relationship with FLA not only offers these microorganisms protection but also enhances their survival outside their hosts and assists in their dispersal across diverse habitats, thereby escalating disease transmission. This review is intended to offer an exhaustive overview of the existing mathematical models that have been applied to understand the dynamics of FLA, especially concerning their interactions with bacteria. An extensive literature review was conducted across Google Scholar, PubMed, and Scopus databases to identify mathematical models that describe the dynamics of interactions between FLA and bacteria, as published in peer‐reviewed scientific journals. The literature search revealed several FLA–bacteria model systems, including Pseudomonas aeruginosa, Pasteurella multocida, and Legionella spp. Although the published mathematical models account for significant system dynamics such as predator–prey relationships and non‐linear growth rates, they generally overlook spatial and temporal heterogeneity in environmental conditions, such as temperature, and population diversity. Future mathematical models will need to incorporate these factors to enhance our understanding of FLA–bacteria dynamics and to provide valuable insights for future risk assessment and disease control measures.

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Section: Simple Differential-equation-based Modelsmentioning

confidence: 99%

Section: A Roadmap For Advancing Understanding Of Fla–bacteria Intera...mentioning

confidence: 99%

Modelling dynamics between free‐living amoebae and bacteria

Ali,

Rice,

Byrne

et al. 2024

Environmental Microbiology

View full text Add to dashboard Cite

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Dynamics of a predator-prey model with strong Allee effect and nonconstant mortality rate

Ye¹,

Wang²,

Jin³

et al. 2022

MBE

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<abstract><p>In this paper, dynamics analysis for a predator-prey model with strong Allee effect and nonconstant mortality rate are taken into account. We systematically studied the existence and stability of the equilibria, and detailedly analyzed various bifurcations, including transcritical, saddle-node, Hopf and Bogdanov-Takens bifurcation. In addition, the theoretical results are verified by numerical simulations. The results indicate that when the mortality is large, the nonconstant death rate can be approximated to a constant value. However, it cannot be considered constant under small mortality rate conditions. Unlike the extinction of species for the constant mortality, the nonconstant mortality may result in the coexistence of prey and predator for the predator-prey model with Allee effect.</p></abstract>

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Spatiotemporal dynamics for impulsive eco-epidemiological model with Crowley-Martin type functional response

Huo¹,

Zhang²,

Hong

2022

MBE

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<abstract><p>Spatiotemporal dynamics of an impulsive eco-epidemiological model with Crowley-Martin type functional responses in a heterogeneous space is studied. The ultimate boundedness of solutions is obtained. The conditions of persistence and extinction under impulsive controls are derived. Furthermore, the existence and globally asymptotic stability of a unique positive periodic solutions are proved. Numerical simulations are also shown to illustrate our theoretical results. Our results show that impulsive harvesting can accelerate the extinction of ecological epidemics.</p></abstract>

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Dynamic Analysis of a Heterogeneous Diffusive Prey-Predator System in Time-Periodic Environment

Cited by 3 publications

References 51 publications

Modelling dynamics between free‐living amoebae and bacteria

Modelling dynamics between free‐living amoebae and bacteria

Dynamics of a predator-prey model with strong Allee effect and nonconstant mortality rate

Spatiotemporal dynamics for impulsive eco-epidemiological model with Crowley-Martin type functional response

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