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19 pages, 805 KB  
Article
Tart Cherry (Prunus cerasus) Extract Exerts High Intracellular ROS Scavenging Activity and Repression of ARE (Antioxidant Response Element) Pathway in Human Hepatocytes
by Cécile Dufour, Mylène Rigal, Camille Gironde, Stephan Plattner and Christophe Furger
Int. J. Mol. Sci. 2025, 26(22), 10827; https://doi.org/10.3390/ijms262210827 - 7 Nov 2025
Viewed by 180
Abstract
Polyphenol-rich fruits represent promising natural candidates for mitigating oxidative stress. We determined in dose–response manner the intracellular antioxidant activities of P. cerasus (tart cherry) extract in HepG2 cells using three different cellular assays targeting specific mechanisms of action: (1) the AOP1 assay, to [...] Read more.
Polyphenol-rich fruits represent promising natural candidates for mitigating oxidative stress. We determined in dose–response manner the intracellular antioxidant activities of P. cerasus (tart cherry) extract in HepG2 cells using three different cellular assays targeting specific mechanisms of action: (1) the AOP1 assay, to assess intracellular ROS scavenging activity; (2) the CAA assay, to estimate ROS scavenging activity at the cell membrane; and (3), the HepG2-ARE-luc assay, to evaluate Antioxidant Response Element (ARE) pathway modulation. Tart cherry extract exhibited a high and concentration-dependent intracellular ROS scavenging activity with the AOP1 assay (EC50 of 72.02 µg/mL), whereas antioxidant efficacy measured via the CAA assay was much lower (EC50 of 6.975 mg/mL). Notably, P. cerasus extract did not activate the ARE-driven luciferase gene expression. Instead, the extract induced a clear dose-dependent repression of ARE-driven transcriptional activity, with a reduction in luciferase gene expression ranging from 20 to 70% across the sample tested concentrations (0.38–98 µg/mL). These findings suggest that, at concentrations where it functions as a potent intracellular ROS scavenger, P. cerasus extract exerts a negative regulation of the ARE pathway. Further investigations are warranted to elucidate the compounds underlying these effects. Full article
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31 pages, 2940 KB  
Article
Global Dynamics and Bifurcation of an Evolutionary Beverton-Holt Model with the Allee Effect
by Emma D’Aniello, Saber Elaydi, Eddy Kwessi, Rafael Luís and Brian Ryals
Symmetry 2025, 17(11), 1811; https://doi.org/10.3390/sym17111811 - 27 Oct 2025
Viewed by 373
Abstract
We study the global dynamics and bifurcation structure of an evolutionary Beverton–Holt model with Allee effects, a framework that couples ecological constraints with adaptive trait evolution. The model accounts for density dependence, mate limitation, and predator saturation, while traits evolve according to selection [...] Read more.
We study the global dynamics and bifurcation structure of an evolutionary Beverton–Holt model with Allee effects, a framework that couples ecological constraints with adaptive trait evolution. The model accounts for density dependence, mate limitation, and predator saturation, while traits evolve according to selection gradients that influence reproduction and competition. From an ecological perspective, we show that weak Allee effects create bistability between extinction and survival, while strong Allee effects generate a critical threshold below which populations collapse and above which they persist at carrying capacity. Evolutionary feedback further reshapes these outcomes by shifting thresholds, modifying stability regions, and producing multiple long-term attractors. Biologically, this reveals how demographic pressures such as scarce mates or high predation interact with trait evolution to determine persistence or extinction, and how adaptive responses may rescue populations facing critical density barriers. Our rigorous analysis and simulations demonstrate that eco–evolutionary processes not only alter classical Beverton–Holt outcomes but also provide insight into mechanisms underlying species persistence, extinction risk, and invasion success under Allee constraints. Full article
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15 pages, 25288 KB  
Article
Reconstructing Ancient Iron-Smelting Furnaces of Guéra (Chad) Through 3D Modeling and AI-Assisted Video Generation
by Jean-Baptiste Barreau, Djimet Guemona and Caroline Robion-Brunner
Electronics 2025, 14(19), 3923; https://doi.org/10.3390/electronics14193923 - 1 Oct 2025
Viewed by 1050
Abstract
This article presents an innovative methodological approach for the documentation and enhancement of ancient ironworking heritage in the Guéra region of Chad. By combining ethno-historical and archaeological surveys, 3D modeling with Blender, and the generation of images and video sequences through artificial intelligence [...] Read more.
This article presents an innovative methodological approach for the documentation and enhancement of ancient ironworking heritage in the Guéra region of Chad. By combining ethno-historical and archaeological surveys, 3D modeling with Blender, and the generation of images and video sequences through artificial intelligence (AI), we propose an integrated production pipeline enabling the faithful reconstruction of three types of metallurgical furnaces. Our method relies on rigorously collected field data to generate multiple and plausible representations from fragmentary information. A standardized evaluation grid makes it possible to assess the archaeological fidelity, cultural authenticity, and visual quality of the reconstructions, thereby limiting biases inherent to generative models. The results offer strong potential for integration into immersive environments, opening up perspectives in education, digital museology, and the virtual preservation of traditional ironworking knowledge. This work demonstrates the relevance of multimodal approaches in reconciling scientific rigor with engaging visual storytelling. Full article
(This article belongs to the Special Issue Augmented Reality, Virtual Reality, and 3D Reconstruction)
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30 pages, 6641 KB  
Article
Cetacean Habitat Use and Occurrence in Fort-de-France Bay (Martinique)
by Coline Violo, Anatole Gros-Martial, Célia Ortolé, Marion Poupard, Morjane Safi and Benjamin de Montgolfier
Animals 2025, 15(18), 2640; https://doi.org/10.3390/ani15182640 - 9 Sep 2025
Viewed by 862
Abstract
While coastal species have been widely studied, active port areas in tropical island regions with intense maritime traffic remain critical, but habitats for cetaceans within the Caribbean have not been thoroughly studied. This study examines the spatial and temporal patterns of habitat use [...] Read more.
While coastal species have been widely studied, active port areas in tropical island regions with intense maritime traffic remain critical, but habitats for cetaceans within the Caribbean have not been thoroughly studied. This study examines the spatial and temporal patterns of habitat use and the characteristics of groups of six cetacean species in the Bay of Fort-de-France in Martinique, an area with heavy marine traffic. Data were collected from 2018 to 2022 through systematic boat-based surveys. We analyzed standardized observations of group occurrence, size, behavior, and depth preference across different subzones of the bay. Our results reveal that Stenella attenuata and Stenella longirostris are the most frequently observed species, exhibiting distinct seasonal patterns, while other species occur more sporadically. Group sizes and behavioral patterns vary significantly across zones and depths. Larger, more interactive groups are generally observed in shallow areas. Several species’ preference for nearshore waters highlights the ecological value of the bay and the potential risks posed by anthropogenic pressures, such as noise, collisions, and habitat degradation. Our findings underscore the importance of considering cetacean habitat use in port management strategies. This study provides essential baseline knowledge to support conservation efforts and the development of mitigation measures that reconcile economic activities with the protection of marine biodiversity. Full article
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31 pages, 1843 KB  
Article
Dynamic Analysis of an Amensalism Model Driven by Multiple Factors: The Interwoven Impacts of Refuge, the Fear Effect, and the Allee Effect
by Yuting Huang, Fengde Chen, Lijuan Chen and Zhong Li
Axioms 2025, 14(8), 567; https://doi.org/10.3390/axioms14080567 - 24 Jul 2025
Viewed by 534
Abstract
This paper investigates a model of amensalism, in which the first species is influenced by the combined effects of refuge and fear, while the second species exhibits an additive Allee effect. The paper analyzes the existence and stability of the equilibria of the [...] Read more.
This paper investigates a model of amensalism, in which the first species is influenced by the combined effects of refuge and fear, while the second species exhibits an additive Allee effect. The paper analyzes the existence and stability of the equilibria of the system and derives the conditions for various bifurcations. In the global structure analysis, the stability at infinity is examined, and the phenomena of global stability and bistability in the system are analyzed. Additionally, a sensitivity analysis is employed to evaluate the impact of system parameters on populations. The study reveals that refuge has a significant positive effect on the first population, and refuge’s effect becomes more pronounced as the fear level increases. Under the strong Allee effect, when the initial density of the second species is low, the second species may eventually become extinct; when the initial density is high, if the refuge parameter is below a certain threshold, increasing the refuge parameter slows down the extinction of the first species, whereas, when the refuge parameter exceeds this threshold, the two species can coexist. Under the weak Allee effect, when the refuge parameter surpasses a certain threshold, the two species can achieve long-term, stable coexistence, and the threshold for the weak Allee effect is higher than that for the strong Allee effect. Full article
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19 pages, 773 KB  
Systematic Review
The Physiopathological Link Between Bisphenol A Exposure and Molar Incisor Hypomineralization Occurrence: A Systematic Review
by Estelle Mathonat, Thibault Canceill, Mathieu Marty, Alison Prosper, Alexia Vinel and Emmanuelle Noirrit-Esclassan
Dent. J. 2025, 13(8), 332; https://doi.org/10.3390/dj13080332 - 22 Jul 2025
Viewed by 973
Abstract
Objective: This study aimed to assess, through a systematic review, the potential link between bisphenol A (BPA) exposure and molar incisor hypomineralization (MIH). Methods: A systematic review was performed according to the PRISMA grid. All international studies—in vitro, in vivo, or [...] Read more.
Objective: This study aimed to assess, through a systematic review, the potential link between bisphenol A (BPA) exposure and molar incisor hypomineralization (MIH). Methods: A systematic review was performed according to the PRISMA grid. All international studies—in vitro, in vivo, or clinical—evaluating the relationships between bisphenol A and MIH were included. An iterative search of eligible publications was conducted on May 26, 2025, using three different databases: PubMed, Science Direct, and Google Scholar. Results: Eleven studies were included in the review, ten of which were experimental studies. They were published between 2013 and 2024. Among the selected articles, a rat model was used in eight studies and seven established a link between MIH and BPA (63.64% of the articles). In the included studies, the incisors of rats treated with BPA presented asymmetrical white spots at the enamel level, with a phenotype similar to human MIH. The authors highlight the hypothesis of the implication of steroid receptors expressed by ameloblasts, in particular at the stage of maturation, thus impacting enamel quality. Conclusions: The results presented in this review highlight a trend in the interaction of bisphenol A with steroid receptors, thus affecting enamel quality. However, these associations are weak, and future studies should investigate cofactors modulating BPA’s role in the development of MIH. Full article
(This article belongs to the Special Issue Current Advances in Pediatric Odontology)
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20 pages, 2678 KB  
Article
The Effects of the Weak Allee Effect and Disease on the Dynamics of a Predator–Prey System: Stability and Bifurcation Properties
by Yurong Dong, Hua Liu, Jianhua Ye, Gang Ma and Yumei Wei
Axioms 2025, 14(7), 531; https://doi.org/10.3390/axioms14070531 - 12 Jul 2025
Viewed by 621
Abstract
In this paper, an eco-epidemiological model with a weak Allee effect and prey disease dynamics is discussed. Mathematical features such as non-negativity, boundedness of solutions, and local stability of the feasible equilibria are discussed. Additionally, the transcritical bifurcation, saddle-node bifurcation, and Hopf bifurcation [...] Read more.
In this paper, an eco-epidemiological model with a weak Allee effect and prey disease dynamics is discussed. Mathematical features such as non-negativity, boundedness of solutions, and local stability of the feasible equilibria are discussed. Additionally, the transcritical bifurcation, saddle-node bifurcation, and Hopf bifurcation are proven using Sotomayor’s theorem and Poincare–Andronov–Hopf theorems. In addition, the correctness of the theoretical analysis is verified by numerical simulation. The numerical simulation results show that the eco-epidemiological model with a weak Allee effect has complex dynamics. If the prey population is not affected by disease, the predator becomes extinct due to a lack of food. Under low infection rates, all populations are maintained in a coexistent state. The Allee effect does not influence this coexistence. At high infection rates, if the prey population is not affected by the Allee effect, the infected prey is found to coexist in an oscillatory state. The predator population and the susceptible prey population will be extinct. If the prey population is affected by the Allee effect, all species will be extinct. Full article
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17 pages, 2060 KB  
Article
Limit Reference Points and Equilibrium Stock Dynamics in the Presence of Recruitment Depensation
by Timothy J. Barrett and Quang C. Huynh
Fishes 2025, 10(7), 342; https://doi.org/10.3390/fishes10070342 - 11 Jul 2025
Viewed by 551
Abstract
Depensation (or an Allee effect) has recently been detected in stock–recruitment relationships (SRRs) in four Atlantic herring stocks and one Atlantic cod stock using a Bayesian statistical approach. In the present study, we define the Allee effect threshold (BAET) for [...] Read more.
Depensation (or an Allee effect) has recently been detected in stock–recruitment relationships (SRRs) in four Atlantic herring stocks and one Atlantic cod stock using a Bayesian statistical approach. In the present study, we define the Allee effect threshold (BAET) for these five stocks and propose BAET as a candidate limit reference point (LRP). We compare BAET to traditional LRPs based on proportions of equilibrium unfished biomass (B0) and biomass at maximum sustainable yield (BMSY) assuming a Beverton–Holt or Ricker SRR with and without depensation, and to the change point from a hockey stick SRR (BCP). The BAET for the case studies exceeded 0.2 B0 and 0.4 BMSY for three of the case study stocks and exceedances of 0.2 B0 were more common when the Ricker form of the SRR was assumed. The BAET estimates for all case studies were less than BCP. When there is depensation in the SRR, multiple equilibrium states can exist when fishing at a fixed fishing mortality rate (F) because the equilibrium recruits-per-spawner line at a given F can intersect the SRR more than once. The equilibrium biomass is determined by whether there is excess recruitment at the initial projected stock biomass. Estimates of equilibrium FMSY in the case studies were generally higher for SRRs that included the depensation parameter; however, the long-term F that would lead the stock to crash (Fcrash) in the depensation SRRs was often about half the Fcrash for SRRs without depensation. When warranted, this study recommends exploration of candidate LRPs from depensatory SRRs, especially if Allee effect thresholds exceed commonly used limits, and simulation testing of management strategies for robustness to depensatory effects. Full article
(This article belongs to the Special Issue Fisheries Monitoring and Management)
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25 pages, 2709 KB  
Article
Dynamics of a Modified Lotka–Volterra Commensalism System Incorporating Allee Effect and Symmetric Non-Selective Harvest
by Kan Fang, Yiqin Wang, Fengde Chen and Xiaoying Chen
Symmetry 2025, 17(6), 852; https://doi.org/10.3390/sym17060852 - 30 May 2025
Viewed by 993
Abstract
This study investigates a modified Lotka–Volterra commensalism system that incorporates the weak Allee effect in prey and symmetric (equal harvesting effort for both species) non-selective harvesting, addressing a critical gap in ecological modeling. Unlike previous work, we rigorously examine how the interaction between [...] Read more.
This study investigates a modified Lotka–Volterra commensalism system that incorporates the weak Allee effect in prey and symmetric (equal harvesting effort for both species) non-selective harvesting, addressing a critical gap in ecological modeling. Unlike previous work, we rigorously examine how the interaction between the Allee effect and harvesting disrupts system stability, giving rise to novel bifurcation phenomena and population collapse thresholds. Using eigenvalue analysis and the Dulac–Bendixson criterion, we derive sufficient conditions for the existence and stability of equilibria. We find that harvesting destabilizes the system by inducing two saddle-node bifurcations. Notably, prey abundance can increase with greater Allee intensity under controlled harvesting—a rare and counterintuitive ecological outcome. Moreover, exceeding a critical harvesting threshold drives both species to extinction, while controlled harvesting allows sustainable coexistence. Numerical simulations support these analytical findings and identify critical parameter ranges for species coexistence. These results contribute to theoretical ecology and offer insights for designing sustainable harvesting strategies that balance exploitation with conservation. Full article
(This article belongs to the Special Issue Mathematics: Feature Papers 2025)
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16 pages, 3443 KB  
Article
On Chaos, Tipping and Delayed Dynamical Transitions in a Hassell-Type Population Model with an Allee Effect
by Jorge Duarte, Cristina Januário and Nuno Martins
Mathematics 2025, 13(8), 1275; https://doi.org/10.3390/math13081275 - 12 Apr 2025
Viewed by 544
Abstract
This study examines abrupt changes in system dynamics, focusing on a Hassell-type density-dependent model with an Allee effect. It aims to analyze tipping points leading to extinction and bistability, including chaotic dynamics. Key methods include computing the topological entropy and Lyapunov exponents when [...] Read more.
This study examines abrupt changes in system dynamics, focusing on a Hassell-type density-dependent model with an Allee effect. It aims to analyze tipping points leading to extinction and bistability, including chaotic dynamics. Key methods include computing the topological entropy and Lyapunov exponents when varying the carrying capacity, the intrinsic growth rate and the initial conditions, providing a detailed characterization of chaotic regimes. Meanwhile, we derive an inverse square-root scaling law near a saddle-node bifurcation using a complex analysis. This study uniquely integrates chaos theory, a bifurcation analysis and scaling laws into a density-dependent ecological model with an Allee effect, revealing how chaotic regimes, bistability and an analytically derived inverse square-root scaling law near extinction shape the tipping point dynamics and critical transitions in ecological systems. Full article
(This article belongs to the Special Issue Dynamical Systems and Complex Systems)
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15 pages, 808 KB  
Article
First Characterization of Nesting Behaviors of Leatherback Turtles (Dermochelys coriacea) and Hawksbill Turtles (Eretmochelys imbricata) in Martinique and Inter-Species Comparison
by Matéa Rossi, Morjane Safi and Benjamin de Montgolfier
Wild 2025, 2(2), 12; https://doi.org/10.3390/wild2020012 - 12 Apr 2025
Viewed by 1578
Abstract
Sea turtles use specific nesting strategies to maximize the survival of their offspring. Few studies have investigated the nesting behavior of leatherback (Dermochelys coriacea) and hawksbill (Eretmochelys imbricata) turtles. The aim of this study was to characterize the nesting [...] Read more.
Sea turtles use specific nesting strategies to maximize the survival of their offspring. Few studies have investigated the nesting behavior of leatherback (Dermochelys coriacea) and hawksbill (Eretmochelys imbricata) turtles. The aim of this study was to characterize the nesting behavior of these two species, taking into account anthropogenic and natural impacts, and to compare behavior between species. Nocturnal monitoring was conducted from 2020 to 2024 on three beaches in Martinique: Madiana, Diamant, and Salines. The average duration of the nesting sequence for leatherback turtles was 101.50 min, with camouflage being the dominant behavior for 27.06% of the total time. For hawksbill turtles, nesting duration was 109.49 min, with digging as the predominant activity (31.68% of total time). No effect of anthropogenic disturbances and obstacles on the behavior of leatherback turtles was observed, while that of hawksbill turtles was significantly influenced by light and the presence of roots. The results revealed behavioral differences between these two species, as well as between two other species: loggerhead (Caretta caretta) and green (Chelonia mydas) turtles. These differences could be explained by morphological differences, nesting habitat peculiarities, beach characteristics, and different evolutionary strategies. Further research is needed to better understand these behaviors and improve conservation efforts. Full article
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20 pages, 323 KB  
Article
Study on Discrete Mosquito Population-Control Models with Allee Effect
by Liang Hong, Yanhua Yang, Wen Zhang, Mingzhan Huang and Xueyong Zhou
Axioms 2025, 14(3), 193; https://doi.org/10.3390/axioms14030193 - 5 Mar 2025
Cited by 1 | Viewed by 771
Abstract
In this study, two discrete mosquito population-control models incorporating the Allee effect are developed to investigate the impact of different sterile mosquito release strategies. By applying the theory of difference equations, a comprehensive analysis is conducted on the existence and stability of fixed [...] Read more.
In this study, two discrete mosquito population-control models incorporating the Allee effect are developed to investigate the impact of different sterile mosquito release strategies. By applying the theory of difference equations, a comprehensive analysis is conducted on the existence and stability of fixed points in scenarios with and without sterile mosquito releases. Conditions for the existence and stability of positive fixed points are rigorously derived. The findings reveal that in the absence of a positive fixed point, the wild mosquito population inevitably declines to extinction. When a single positive fixed point exists, the population dynamics exhibit dependence on the initial population size, potentially leading to either extinction or stabilization. In cases where two positive fixed points are present, a bistable dynamic emerges, indicating the coexistence of two mosquito populations. Full article
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15 pages, 3440 KB  
Article
Contribution of Structure Learning Algorithms in Social Epidemiology: Application to Real-World Data
by Helene Colineaux, Benoit Lepage, Pierre Chauvin, Chloe Dimeglio, Cyrille Delpierre and Thomas Lefèvre
Int. J. Environ. Res. Public Health 2025, 22(3), 348; https://doi.org/10.3390/ijerph22030348 - 27 Feb 2025
Viewed by 869
Abstract
Epidemiologists often handle large datasets with numerous variables and are currently seeing a growing wealth of techniques for data analysis, such as machine learning. Critical aspects involve addressing causality, often based on observational data, and dealing with the complex relationships between variables to [...] Read more.
Epidemiologists often handle large datasets with numerous variables and are currently seeing a growing wealth of techniques for data analysis, such as machine learning. Critical aspects involve addressing causality, often based on observational data, and dealing with the complex relationships between variables to uncover the overall structure of variable interactions, causal or not. Structure learning (SL) methods aim to automatically or semi-automatically reveal the structure of variables’ relationships. The objective of this study is to delineate some of the potential contributions and limitations of structure learning methods when applied to social epidemiology topics and the search for determinants of healthcare system access. We applied SL techniques to a real-world dataset, namely the 2010 wave of the SIRS cohort, which included a sample of 3006 adults from the Paris region, France. Healthcare utilization, encompassing both direct and indirect access to care, was the primary outcome. Candidate determinants included health status, demographic characteristics, and socio-cultural and economic positions. We present two approaches: a non-automated epidemiological method (an initial expert knowledge network and stepwise logistic regression models) and three SL techniques using various algorithms, with and without knowledge constraints. We compared the results based on the presence, direction, and strength of specific links within the produced network. Although the interdependencies and relative strengths identified by both approaches were similar, the SL algorithms detect fewer associations with the outcome than the non-automated method. Relationships between variables were sometimes incorrectly oriented when using a purely data-driven approach. SL algorithms can be valuable in exploratory stages, helping to generate new hypotheses or mining novel databases. However, results should be validated against prior knowledge and supplemented with additional confirmatory analyses. Full article
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30 pages, 978 KB  
Article
A Mathematical Perspective on the Influence of Allee Effects in Oncolytic Virotherapy
by Eymard Hernández-López and Jin Wang
Mathematics 2025, 13(5), 744; https://doi.org/10.3390/math13050744 - 25 Feb 2025
Cited by 1 | Viewed by 1067
Abstract
This article is concerned with the mathematical modeling of cancer virotherapy, emphasizing the impact of Allee effects on tumor cell growth. We propose a modeling framework that describes the complex interaction between tumor cells and oncolytic viruses. The efficacy of this therapy against [...] Read more.
This article is concerned with the mathematical modeling of cancer virotherapy, emphasizing the impact of Allee effects on tumor cell growth. We propose a modeling framework that describes the complex interaction between tumor cells and oncolytic viruses. The efficacy of this therapy against cancer is mathematically investigated. The analysis involves linear and logistic growth scenarios coupled with different Allee effects, including weak, strong, and hyper Allee forms. Critical points are identified, and their existence and stability are analyzed using dynamical system theories and bifurcation techniques. Also, bifurcation diagrams and numerical simulations are utilized to verify and extend analytical results. It is observed that Allee effects significantly influence the stability of the system and the conditions necessary for tumor control and eradication. Full article
(This article belongs to the Special Issue Mathematical Modeling and Data Science for Biology and Medicine)
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19 pages, 2159 KB  
Article
Impact of the Allee Effect on the Dynamics of a Predator–Prey Model Exhibiting Group Defense
by Manoj Kumar Singh, Arushi Sharma and Luis M. Sánchez-Ruiz
Mathematics 2025, 13(4), 633; https://doi.org/10.3390/math13040633 - 14 Feb 2025
Cited by 1 | Viewed by 1093
Abstract
The Allee effect and group defense are two naturally occurring phenomena in the prey species of a predator–prey system. This research paper examines the impact of integrating the Allee effect on the dynamics of a predator–prey model, including a density-dependent functional response that [...] Read more.
The Allee effect and group defense are two naturally occurring phenomena in the prey species of a predator–prey system. This research paper examines the impact of integrating the Allee effect on the dynamics of a predator–prey model, including a density-dependent functional response that reflects the defensive strategies of the prey population. Initially, the positivity and boundedness of the solutions are examined to ascertain the biological validity of the model. The presence of ecologically significant equilibrium points are established, followed by examining parametric restrictions for the local stability to comprehend the system dynamics in response to minor perturbations. A detailed computation encompasses diverse bifurcations, both of codimension one and two, which provide distinct dynamic behaviors of the model, such as oscillations, stable coexistence, and potential extinction scenarios. Numerical simulation has been provided to showcase complex dynamical behavior resulting from the Allee effect and prey group defense. Full article
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