Abstract. During the COVID-19 pandemic, the most important thing was to control the overall infection rate. To achieve this goal, social managers can choose to use vaccines with different production cycles and therapeutic effects for epidemic prevention and control under financial budget constraints. We adopt a two-tier queueing system with reneging to characterize the operation management of COVID19 vaccine ordering and vaccination, in which a higher-efficacy vaccine queue (HQ) and a lower-efficacy vaccine queue (LQ) are employed to account for two types of vaccines service. In light of this framework, a recursive formula is proposed for deriving the infection rates of residents in both HQ and LQ. Social managers can achieve the lowest total infection rate by selecting appropriate vaccine ordering strategies under fixed service capacity, or by allocating financial budgets reasonably under the investment cost regime. Accordingly, we obtain socially optimal vaccine ordering strategies and financial budget allocation. Finally, we analyze the sensitivity of various parameters to relevant optimal strategies and discover that utilizing a mixed ordering strategy is socially optimal in most circumstances. However, in some extreme cases, ordering a single type of vaccine (higher- or lower-efficacy) may result in the lowest societal infection rate.
{"title":"Optimal Ordering Strategy and Budget Allocation for the COVID-19 Vaccination Planning","authors":"Xueping Liu, Sheng Zhu, Jinting Wang","doi":"10.1051/mmnp/2024002","DOIUrl":"https://doi.org/10.1051/mmnp/2024002","url":null,"abstract":"Abstract. During the COVID-19 pandemic, the most important thing was to control the overall infection rate. To achieve this goal, social managers can choose to use vaccines with different production cycles and therapeutic effects for epidemic prevention and control under financial budget constraints. We adopt a two-tier queueing system with reneging to characterize the operation management of COVID19 vaccine ordering and vaccination, in which a higher-efficacy vaccine queue (HQ) and a lower-efficacy vaccine queue (LQ) are employed to account for two types of vaccines service. In light of this framework, a recursive formula is proposed for deriving the infection rates of residents in both HQ and LQ. Social managers can achieve the lowest total infection rate by selecting appropriate vaccine ordering strategies under fixed service capacity, or by allocating financial budgets reasonably under the investment cost regime. Accordingly, we obtain socially optimal vaccine ordering strategies and financial budget allocation. Finally, we analyze the sensitivity of various parameters to relevant optimal strategies and discover that utilizing a mixed ordering strategy is socially optimal in most circumstances. However, in some extreme cases, ordering a single type of vaccine (higher- or lower-efficacy) may result in the lowest societal infection rate.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139785522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract. During the COVID-19 pandemic, the most important thing was to control the overall infection rate. To achieve this goal, social managers can choose to use vaccines with different production cycles and therapeutic effects for epidemic prevention and control under financial budget constraints. We adopt a two-tier queueing system with reneging to characterize the operation management of COVID19 vaccine ordering and vaccination, in which a higher-efficacy vaccine queue (HQ) and a lower-efficacy vaccine queue (LQ) are employed to account for two types of vaccines service. In light of this framework, a recursive formula is proposed for deriving the infection rates of residents in both HQ and LQ. Social managers can achieve the lowest total infection rate by selecting appropriate vaccine ordering strategies under fixed service capacity, or by allocating financial budgets reasonably under the investment cost regime. Accordingly, we obtain socially optimal vaccine ordering strategies and financial budget allocation. Finally, we analyze the sensitivity of various parameters to relevant optimal strategies and discover that utilizing a mixed ordering strategy is socially optimal in most circumstances. However, in some extreme cases, ordering a single type of vaccine (higher- or lower-efficacy) may result in the lowest societal infection rate.
{"title":"Optimal Ordering Strategy and Budget Allocation for the COVID-19 Vaccination Planning","authors":"Xueping Liu, Sheng Zhu, Jinting Wang","doi":"10.1051/mmnp/2024002","DOIUrl":"https://doi.org/10.1051/mmnp/2024002","url":null,"abstract":"Abstract. During the COVID-19 pandemic, the most important thing was to control the overall infection rate. To achieve this goal, social managers can choose to use vaccines with different production cycles and therapeutic effects for epidemic prevention and control under financial budget constraints. We adopt a two-tier queueing system with reneging to characterize the operation management of COVID19 vaccine ordering and vaccination, in which a higher-efficacy vaccine queue (HQ) and a lower-efficacy vaccine queue (LQ) are employed to account for two types of vaccines service. In light of this framework, a recursive formula is proposed for deriving the infection rates of residents in both HQ and LQ. Social managers can achieve the lowest total infection rate by selecting appropriate vaccine ordering strategies under fixed service capacity, or by allocating financial budgets reasonably under the investment cost regime. Accordingly, we obtain socially optimal vaccine ordering strategies and financial budget allocation. Finally, we analyze the sensitivity of various parameters to relevant optimal strategies and discover that utilizing a mixed ordering strategy is socially optimal in most circumstances. However, in some extreme cases, ordering a single type of vaccine (higher- or lower-efficacy) may result in the lowest societal infection rate.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139845369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Zhenmin Fan, Jiangliang Yao, Jianda Xu, Xiao Liu, Mingyuan Liu, Xia Ye, Xiaoyan Deng
Stent restenosis and late thrombosis compromise endovascular stent implantation clinical benefit, and the mechanism is unclear. Since nitric oxide (NO) plays a pivotal role in maintaining vascular homeostasis, we believe that stenting can affect NO concentration in the host artery, thereby contributing to postoperative adverse events. We numerically investigated NO concentration after stenting based on the patient-specific carotid to verify this hypothesis. The simulation revealed that stent implantation caused blood flow disturbance, a low wall shear stress, and a significant decrease in NO on the luminal surface, especially in the region of the stented segment. Moreover, severe damage to the artery wall or low blood flow, leading to a low NO generation rate, would induce relatively low NO level in the stented segment. Additionally, we demonstrated that NO distribution might be affected by the combination of stent struts and carotid bifurcation geometry, while the host arterial configuration might play a leading role in the distribution of NO concentration. In conclusion, the carotid artery had a relatively low NO concentration level near stent struts, especially at the severely injured artery, low blood flow, long stenting, and complex host artery which might lead to a genesis/development of adverse events after that intervention.
支架再狭窄和晚期血栓形成损害了血管内支架植入术的临床疗效，其机制尚不清楚。由于一氧化氮（NO）在维持血管稳态中起着关键作用，我们认为支架植入术会影响宿主动脉中的一氧化氮浓度，从而导致术后不良事件的发生。为了验证这一假设，我们基于患者特异性颈动脉对支架植入后的 NO 浓度进行了数值研究。模拟结果显示，支架植入导致血流紊乱、管壁剪应力降低，管腔表面的 NO 显著减少，尤其是在支架段区域。此外，动脉壁的严重破坏或低血流量导致 NO 生成率低，也会引起支架区段的 NO 水平相对较低。此外，我们还证明，NO 的分布可能会受到支架支柱和颈动脉分叉几何形状组合的影响，而宿主动脉的构造可能会在 NO 浓度的分布中起主导作用。总之，颈动脉支架支柱附近的 NO 浓度水平相对较低，尤其是在严重损伤的动脉、低血流量、长支架和复杂的宿主动脉处，这可能会导致介入治疗后不良事件的发生/发展。
{"title":"Nitric oxide transport in carotid bifurcation after different stent interventions: a numerical study","authors":"Zhenmin Fan, Jiangliang Yao, Jianda Xu, Xiao Liu, Mingyuan Liu, Xia Ye, Xiaoyan Deng","doi":"10.1051/mmnp/2023039","DOIUrl":"https://doi.org/10.1051/mmnp/2023039","url":null,"abstract":"Stent restenosis and late thrombosis compromise endovascular stent implantation clinical benefit, and the mechanism is unclear. Since nitric oxide (NO) plays a pivotal role in maintaining vascular homeostasis, we believe that stenting can affect NO concentration in the host artery, thereby contributing to postoperative adverse events. We numerically investigated NO concentration after stenting based on the patient-specific carotid to verify this hypothesis. The simulation revealed that stent implantation caused blood flow disturbance, a low wall shear stress, and a significant decrease in NO on the luminal surface, especially in the region of the stented segment. Moreover, severe damage to the artery wall or low blood flow, leading to a low NO generation rate, would induce relatively low NO level in the stented segment. Additionally, we demonstrated that NO distribution might be affected by the combination of stent struts and carotid bifurcation geometry, while the host arterial configuration might play a leading role in the distribution of NO concentration. In conclusion, the carotid artery had a relatively low NO concentration level near stent struts, especially at the severely injured artery, low blood flow, long stenting, and complex host artery which might lead to a genesis/development of adverse events after that intervention.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139215133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
S. Chabbar, A. Habbal, R. Aboulaich, Nabil Ismaili, Sanaa El Majjaoui
Prostate cancer is a hormone-dependent cancer characterized by two types of cancer cells, androgen-dependent cancer cells and androgen-resistant ones. The objective of this paper is to present a novel mathematical model for the treatment of prostate cancer under combined hormone therapy and brachytherapy. Using a system of partial differential equations, we quantify and study the evolution of the different cell densities involved in prostate cancer and their responses to the two treatments. Numerical simulations of tumor growth under different therapeutic strategies are explored and presented. The numerical simulations are carried out on FreeFem++ using a 2D finite element method.
{"title":"COMBINED HORMONE AND BRACHY THERAPIES FOR THE TREATMENT OF PROSTATE CANCER","authors":"S. Chabbar, A. Habbal, R. Aboulaich, Nabil Ismaili, Sanaa El Majjaoui","doi":"10.1051/mmnp/2023038","DOIUrl":"https://doi.org/10.1051/mmnp/2023038","url":null,"abstract":"Prostate cancer is a hormone-dependent cancer characterized by two types of cancer cells, androgen-dependent cancer cells and androgen-resistant ones. The objective of this paper is to present a novel mathematical model for the treatment of prostate cancer under combined hormone therapy and brachytherapy. Using a system of partial differential equations, we quantify and study the evolution of the different cell densities involved in prostate cancer and their responses to the two treatments. Numerical simulations of tumor growth under different therapeutic strategies are explored and presented. The numerical simulations are carried out on FreeFem++ using a 2D finite element method.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139264994","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider the governing equations for the motion of the viscous fluids in two moving domains and an evolving surface from both energetic and thermodynamic points of view. We make mathematical models for multiphase flow with surface flow by our energetic variational and thermodynamic approaches. More precisely, we apply our energy densities, the first law of thermodynamics, and the law of conservation of total energy to derive our multiphase flow system with surface tension and flow. We study the conservative forms and conservation laws of our system by using the surface transport theorem and integration by parts. Moreover, we investigate the enthalpy, the entropy, the Helmholtz free energy, and the Gibbs free energy of our model by applying the thermodynamic identity. The key idea of deriving surface tension and viscosities is to make use of both the first law of thermodynamics and our energy densities.
{"title":"Thermodynamical Modeling of Multiphase Flow System with Surface Tension and Flow","authors":"Hajime Koba","doi":"10.1051/mmnp/2023036","DOIUrl":"https://doi.org/10.1051/mmnp/2023036","url":null,"abstract":"We consider the governing equations for the motion of the viscous fluids in two moving domains and an evolving surface from both energetic and thermodynamic points of view. We make mathematical models for multiphase flow with surface flow by our energetic variational and thermodynamic approaches. More precisely, we apply our energy densities, the first law of thermodynamics, and the law of conservation of total energy to derive our multiphase flow system with surface tension and flow. We study the conservative forms and conservation laws of our system by using the surface transport theorem and integration by parts. Moreover, we investigate the enthalpy, the entropy, the Helmholtz free energy, and the Gibbs free energy of our model by applying the thermodynamic identity. The key idea of deriving surface tension and viscosities is to make use of both the first law of thermodynamics and our energy densities.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135220402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Juan A. Aledo, Carlos Andreu-Vilarroig, Juan-Carlos Cortés, Juan C. Orengo, Rafael-Jacinto Villanueva
Antibiotic resistance is one of the greatest public health threats today, mainly due to the non-rational use of antibiotics. Some of these microorganisms, such as Acinetobacter baumannii, which are especially problematic in hospitals, have rapidly developed resistance and only a few last-resort antibiotics, such as colistin, are effective against them. In this work we propose a random agent-based model to describe the evolution of colistin-resistant A. baumannii in the population of Valencia city (Spain) and to predict its impact both on the whole population and by age groups. The model consists of a synthetic population whose agents evolve over time by changing their state variables randomly, based on a set of conditional probabilities, simulating the pathogen infection process. The model has been calibrated with real epidemiological data and, with the best parameters found, simulations and predictions about the incidence and the absolute cases of colistin-resistan A. baumannii have been carried out for the coming years. Results suggest that the evolution of the proportion of resistance will be exponential, exceeding 50% around 2025, and it will affect people over 60 years old more severely in terms of the number of cases.
{"title":"On the epidemiological evolution of colistin-resistant Acinetobacter baumannii in the city of Valencia: an agent-based modelling approach","authors":"Juan A. Aledo, Carlos Andreu-Vilarroig, Juan-Carlos Cortés, Juan C. Orengo, Rafael-Jacinto Villanueva","doi":"10.1051/mmnp/2023037","DOIUrl":"https://doi.org/10.1051/mmnp/2023037","url":null,"abstract":"Antibiotic resistance is one of the greatest public health threats today, mainly due to the non-rational use of antibiotics. Some of these microorganisms, such as Acinetobacter baumannii, which are especially problematic in hospitals, have rapidly developed resistance and only a few last-resort antibiotics, such as colistin, are effective against them. In this work we propose a random agent-based model to describe the evolution of colistin-resistant A. baumannii in the population of Valencia city (Spain) and to predict its impact both on the whole population and by age groups. The model consists of a synthetic population whose agents evolve over time by changing their state variables randomly, based on a set of conditional probabilities, simulating the pathogen infection process. The model has been calibrated with real epidemiological data and, with the best parameters found, simulations and predictions about the incidence and the absolute cases of colistin-resistan A. baumannii have been carried out for the coming years. Results suggest that the evolution of the proportion of resistance will be exponential, exceeding 50% around 2025, and it will affect people over 60 years old more severely in terms of the number of cases.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135220405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper a model of tumor-immune response for chronic myeloid leukemia (CML) is proposed and analyzed. It is based on the ordinary differential equations' models (ODE) studied in former works. The proliferation of cells, their differentiation in the bone marrow and the interactions of leukemic and immune cells are described. The model is based on a non-monotonic immune response. At low levels immune response increases with the tumor load, whereas at high levels tumor is suppressing the effect of the immune system (immunosuppression). We consider that the age of cells is described by a continuous variable which we use to structure the system and obtain a partial differential equations' model (PDEs). We analyze the stability of the equilibrium points of the model and compare it to the case where age was described as a discrete state. In particular, an equilibrium point describing remission, induced by a control of the immune system, is shown to be unstable in certain situations for the PDE model, whereas in the ODE case, it was systematically stable.
{"title":"Influence of the age structure on the stability in a tumor-immune model for chronic myeloid leukemia","authors":"Kyriaki Dariva, Thomas Lepoutre","doi":"10.1051/mmnp/2023034","DOIUrl":"https://doi.org/10.1051/mmnp/2023034","url":null,"abstract":"In this paper a model of tumor-immune response for chronic myeloid leukemia (CML) is proposed and analyzed. It is based on the ordinary differential equations' models (ODE) studied in former works. The proliferation of cells, their differentiation in the bone marrow and the interactions of leukemic and immune cells are described. The model is based on a non-monotonic immune response. At low levels immune response increases with the tumor load, whereas at high levels tumor is suppressing the effect of the immune system (immunosuppression). We consider that the age of cells is described by a continuous variable which we use to structure the system and obtain a partial differential equations' model (PDEs). We analyze the stability of the equilibrium points of the model and compare it to the case where age was described as a discrete state. In particular, an equilibrium point describing remission, induced by a control of the immune system, is shown to be unstable in certain situations for the PDE model, whereas in the ODE case, it was systematically stable.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135823691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract. In this work, we consider a Becker-Döring-like mathematical interaction model between Aβ-monomers and Aβ proto-oligomers playing an important role in Alzheimer’s disease. In this context, the clustering process where two or more Aβ-monomers spontaneously aggregate and form a seed of proto-oligomers is highlighted. We prove the quadratic well-posedness [4] of the problem associated with the estimation of clustering rate µ from measured data at different times.
{"title":"Q-well-posedness of an A$beta$-protein polymerization model","authors":"Léon Matar Tine, Cheikh Gueye, Laurent Pujo-Menjouet, Sorin Ionel Ciuperca","doi":"10.1051/mmnp/2023028","DOIUrl":"https://doi.org/10.1051/mmnp/2023028","url":null,"abstract":"Abstract. In this work, we consider a Becker-Döring-like mathematical interaction model between Aβ-monomers and Aβ proto-oligomers playing an important role in Alzheimer’s disease. In this context, the clustering process where two or more Aβ-monomers spontaneously aggregate and form a seed of proto-oligomers is highlighted. We prove the quadratic well-posedness [4] of the problem associated with the estimation of clustering rate µ from measured data at different times.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134885427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider a one-dimensional model of hemodynamics for a tube defined by a Koiter shell, and investigate traveling wave solutions. The system of partial differential equations is reduced to a fourth-order ordinary differential equation for such solutions. We find a single equilibrium point and determine the condition for the changing type of the equilibria for the corresponding system of first-order differential equations. The conditions for changing the type of the equilibrium point are formulated. Then we introduce the classification of blood flow regimes relative to the type of the equilibrium point. Numerical experiments are carried out to confirm and analyze the obtained results, various regimes of blood flow are considered.
{"title":"TRAVELING WAVES IN HEMODYNAMIC EQUATIONS WITH THE KOITER SHELL","authors":"Sergey Vasyutkin, Alexander Chupakhin","doi":"10.1051/mmnp/2023032","DOIUrl":"https://doi.org/10.1051/mmnp/2023032","url":null,"abstract":"We consider a one-dimensional model of hemodynamics for a tube defined by a Koiter shell, and investigate traveling wave solutions. The system of partial differential equations is reduced to a fourth-order ordinary differential equation for such solutions. We find a single equilibrium point and determine the condition for the changing type of the equilibria for the corresponding system of first-order differential equations. The conditions for changing the type of the equilibrium point are formulated. Then we introduce the classification of blood flow regimes relative to the type of the equilibrium point. Numerical experiments are carried out to confirm and analyze the obtained results, various regimes of blood flow are considered.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135769638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose a general population dynamics model for two seagrass species growing and interacting in two spatial dimensions. The model includes spatial terms accounting for the clonal growth characteristics of seagrasses, and coupling between species through the net mortality rate. We consider both intraspecies and interspecies facilitative and competitive interactions, allowing density-dependent interaction mechanisms. Here we study the case of very similar species with reciprocal interactions, which allows reducing the number of the model parameters to just four, and whose bifurcation structure can be considered the backbone of the complete system. We find that the parameter space can be divided into ten regions with qualitatively different bifurcation diagrams. These regimes can be further grouped into just five regimes with different ecological interpretations. Our analysis allows the classification of all possible density distributions and dynamical behaviors of meadows with two coexisting species.
{"title":"A model for seagrass species competition: dynamics of the symmetric case.","authors":"Pablo Moreno-Spiegelberg, Damià Gomila","doi":"10.1051/mmnp/2023033","DOIUrl":"https://doi.org/10.1051/mmnp/2023033","url":null,"abstract":"We propose a general population dynamics model for two seagrass species growing and interacting in two spatial dimensions. The model includes spatial terms accounting for the clonal growth characteristics of seagrasses, and coupling between species through the net mortality rate. We consider both intraspecies and interspecies facilitative and competitive interactions, allowing density-dependent interaction mechanisms. Here we study the case of very similar species with reciprocal interactions, which allows reducing the number of the model parameters to just four, and whose bifurcation structure can be considered the backbone of the complete system. We find that the parameter space can be divided into ten regions with qualitatively different bifurcation diagrams. These regimes can be further grouped into just five regimes with different ecological interpretations. Our analysis allows the classification of all possible density distributions and dynamical behaviors of meadows with two coexisting species.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136011697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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