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Mathematical Modelling of Natural Phenomena最新文献

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Interaction between crowding and growth in tumours with stem cells: conceptual mathematical modelling 肿瘤干细胞拥挤和生长之间的相互作用：概念数学模型
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2023-03-17 DOI: 10.1051/mmnp/2023011
L. Meacci, M. Primicerio
{"title":"Interaction between crowding and growth in tumours with stem cells: conceptual mathematical modelling","authors":"L. Meacci, M. Primicerio","doi":"10.1051/mmnp/2023011","DOIUrl":"https://doi.org/10.1051/mmnp/2023011","url":null,"abstract":"The paper proposes a conceptual modelling of growth of tumours in presence of immortal multipotent cancer stem cells (CSCs) and several lineages of differentiated tumour cells (CCs).\u0000The replication of CSCs is assumed symmetric or asymmetric with a prescribed mean ratio and mitosis and apoptosis are taken into account for the CCs aging. Replication can be hindered by the local crowding of the cells.\u0000The model is implemented in the framework of 3D cellular automata (CA) whose dynamics is governed by stochastic rules. Simulations are displayed showing the growth of a tumour and the fractions of different lineages and age classes of CCs.\u0000Then, an approach that considers the same dynamics of aging, replication, and apoptosis, but studying the time evolution of the fractions of the different lineages and age classes of cells averaged over the total volume is presented. The dynamics is governed by a system of ordinary differential equations (ODEs), hence by deterministic rules. Numerical simulations of the solution of this system show qualitative similarity with the CA results, although the crowding effect is no longer a local effect, but averaged over the total volume. The proof of the mathematical well-posedness of this model is provided.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46708487","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}
引用次数: 0
Qualitative analysis for a diffusive predator-prey model with hunting cooperation and Holling type textrm{III}  functional response 具有狩猎合作和Holling型功能反应的扩散捕食-被捕食模型的定性分析
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2023-03-05 DOI: 10.1051/mmnp/2023010
I. Benamara, A. El abdllaoui, R. Yafia, H. Dutta
{"title":"Qualitative analysis for a diffusive predator-prey model with hunting cooperation and Holling type textrm{III}  functional response","authors":"I. Benamara, A. El abdllaoui, R. Yafia, H. Dutta","doi":"10.1051/mmnp/2023010","DOIUrl":"https://doi.org/10.1051/mmnp/2023010","url":null,"abstract":"The Spatio-temporal pattern induced by self-diffusion of a predator-prey model with Holling type III functional response that incorporates the hunting cooperation between predators has been investigated in this paper. For the local model without structure, stability of non-negative equilibria with or without collaborative hunting in predators is studied. For the Spatio-temporal model, we analyze the effect of hunting cooperation term on diffusion-driven Turing instability of the homogeneous positive equilibria. To get an idea about patterns formation near the Turing bifurcation, we derive and give a detailed study of the amplitude equation using the multiple-scale analysis. Our result shows that hunting cooperation plays a crucial role in determining the stability and the Turing bifurcation of the model, which is in sharp contrast to the case without cooperation in hunting. Furthermore, some numerical simulations are illustrated to visualize the complex dynamic behavior of the model.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43064114","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}
引用次数: 0
MODELLING OF HILLSLOPE STORAGE UNDER TEMPORALLY VARIED RAINFALL RECHARGE 降雨补给随时间变化的山坡蓄水模型
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2023-03-02 DOI: 10.1051/mmnp/2023009
P. Hsieh, Tzu-Ting Huang
{"title":"MODELLING OF HILLSLOPE STORAGE UNDER TEMPORALLY VARIED RAINFALL RECHARGE","authors":"P. Hsieh, Tzu-Ting Huang","doi":"10.1051/mmnp/2023009","DOIUrl":"https://doi.org/10.1051/mmnp/2023009","url":null,"abstract":"Water storage inside hillslopes is a crucial issue of environment and water resources. This study separately built a numerical model and an analytical model employing a hillslope-storage equation to simulate the water storage in a sloping aquifer response to recharge. The variable width of hillslope was hypothetically represented by an exponential function to categorize the hillslope into three types: uniform, convergent, and divergent. An integral transform technique was introduced to derive the analytical solution whereas a finite difference method was employed for the numerical modelling. As a result, under the same scenario a gap existed between the two solutions to distinct forms of the water storage equation, and the gap decreases with a falling recharge rate for convergent hillslopes. Moreover, all outflows gradually approached one value based on different hillslopes under the same accumulative recharge amount for six typical rainfall recharge patterns. Particularly, while the recharge stops, the outflow decreases and then mildly rises for a long time for convergent hillslope because of the slow water release near the upstream boundary where the storage water is relatively abundant due to the widest width.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44313701","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}
引用次数: 1
How do cell crowding and starvation affect avascular tumor growth of the EMT6/Ro tumor? 细胞拥挤和饥饿如何影响EMT6/Ro肿瘤的无血管肿瘤生长？
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2023-02-16 DOI: 10.1051/mmnp/2023007
Bjarke Spangsberg Bak, Morten Andersen, J. Ottesen, Jesper Schmidt Hansen
{"title":"How do cell crowding and starvation affect avascular tumor growth of the EMT6/Ro tumor?","authors":"Bjarke Spangsberg Bak, Morten Andersen, J. Ottesen, Jesper Schmidt Hansen","doi":"10.1051/mmnp/2023007","DOIUrl":"https://doi.org/10.1051/mmnp/2023007","url":null,"abstract":"Here we re-examine experimental in vitro data for the EMT6/Ro tumor volume and viable rim thickness. This shows that the growth speed is constant in time, and independent of nutrient concentration at large concentrations, but that the viable rim thickness increases in this high concentration regime. We then present a simple mechanistic reaction-diffusion equation that includes crowding and starvation effects, and show that the model qualitatively captures the experimental observations. Moreover, the model predicts that the cancer cell concentration is characterised by a wave pulse (soliton), and the pulse shape is explored through zero’th order perturbation analysis corresponding to large wave speeds. It is shown that this zero’th order term is dominant for the experimental condition, further indicating that the non-linear reaction governs the pulse characteristic shape. Finally, at low nutrient concentrations we find that the front is a pulled-front, that is, the growth speed is determined by the cell multiplication at the wave front edge in accordance with earlier modelling approaches.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42480966","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}
引用次数: 0
Traveling solutions for a multi-anticipative car-following traffic model 多预期车辆跟随交通模型的出行解决方案
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2023-02-12 DOI: 10.1051/mmnp/2023006
Nader El Khatib, Amine Ghorbel, Agatha Joumaa, Mamdouh Zaydan
{"title":"Traveling solutions for a multi-anticipative car-following traffic model","authors":"Nader El Khatib, Amine Ghorbel, Agatha Joumaa, Mamdouh Zaydan","doi":"10.1051/mmnp/2023006","DOIUrl":"https://doi.org/10.1051/mmnp/2023006","url":null,"abstract":"In this paper, we consider a steady state multi-anticipative traffic model and we provide necessarily and sufficient conditions for the existence of traveling solutions. In our work, the word \"traveling\" means that the distance between two consecutive vehicles travels continuously between two different states. As application to our result, we show that taking a strictly concave optimal velocity, we can construct a traveling solution such that the distance between two vehicles decreases. The existence, uniqueness and the study of the asymptotic behavior of such solutions is done at the level of the Hamilton-Jacobi equation.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44366224","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}
引用次数: 0
Mathematical Modelling of the Effects of Statins on the Growth of Necrotic Core in Atherosclerotic Plaque 他汀类药物对动脉粥样硬化斑块坏死核心生长影响的数学模型
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2023-02-09 DOI: 10.1051/mmnp/2023005
Weirui Lei, Ji-wen Hu, Yaxian Xie, Can Liu, Xuekun Chen
{"title":"Mathematical Modelling of the Effects of Statins on the Growth of Necrotic Core in Atherosclerotic Plaque","authors":"Weirui Lei, Ji-wen Hu, Yaxian Xie, Can Liu, Xuekun Chen","doi":"10.1051/mmnp/2023005","DOIUrl":"https://doi.org/10.1051/mmnp/2023005","url":null,"abstract":"A large necrotic core increases the risk of atherosclerotic plaque instability. Statins can delay the growth of necrotic core in plaques, but the kinetic mechanism of statins in slowing down the necrotic core has not yet been addressed in detail. In this paper, a mathematical model is governed by a system of advection-diffusion-reaction equations coupling of the porous nature of vessel wall is established and applied to illustrate the plaque growth with lipid-rich necrotic core (LRNC) with and without statins using finite element method. We study the influence of LRNC plaque growth for different drug concentrations at different time intervals. The results showed that the drug use at different time points has a significant impact on the treatment efficacy. Compared with  short-term, low-dose treatment, early statin treatment with high dose showed more pronounced effects on reducing the low-density lipoprotein (LDL) cholesterol, decreasing the volume of necrotic core, changing the characteristics of plaques, and improving the plaque stability. The model is validated by comparing with the clinical data, and may be used to predict the progression of LRNC plaque and the effects of statin therapy.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44110722","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}
引用次数: 1
Threshold Behavior of an Age-structured Tumor Immune Model 年龄结构肿瘤免疫模型的阈值行为
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2023-01-30 DOI: 10.1051/mmnp/2023001
Zhong Luo, Zijian Liu, Yuanshun Tan, Jin Yang, Huanhuan Qiu
{"title":"Threshold Behavior of an Age-structured Tumor Immune Model","authors":"Zhong Luo, Zijian Liu, Yuanshun Tan, Jin Yang, Huanhuan Qiu","doi":"10.1051/mmnp/2023001","DOIUrl":"https://doi.org/10.1051/mmnp/2023001","url":null,"abstract":"In this paper, we present and analyze an age-structured tumor immune model. Based on the fact that tumor cells of different ages tend to exhibit different physiological behaviors, we consider the age structure of tumor cells, age-based proliferation function and age-dependent death function in the model. The threshold $mathfrak{R}_{0}$ for the existence of tumor-free steady state is derived. It is found that if $mathfrak{R}_{0}<1$, the tumor-free steady state is not only locally stable but also globally stable. Moreover, numerical simulation shows that the threshold $mathfrak{R}_{0}$ may be regarded as an index to reflect the ability of ``tumor immune surveillance\", ie, the smaller the $mathfrak{R}_{0}$, the better the ability of tumor immune surveillance. If $mathfrak{R}_{0}>1$, it is proved that the tumor steady state is existent  and uniformly persistent. The local stability of the tumor steady state is investigated under some further conditions besides $mathfrak{R}_{0}>1$. In the end, we estimate the system parameters, verify the theoretical results and analyze some system  parameters' sensitivities.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48141211","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}
引用次数: 0
The effect of connecting sites in the environment of a harvested population 收获种群环境中连接位点的影响
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2023-01-23 DOI: 10.1051/mmnp/2023004
R. Bravo de la Parra, J. Poggiale, P. Auger
{"title":"The effect of connecting sites in the environment of a harvested population","authors":"R. Bravo de la Parra, J. Poggiale, P. Auger","doi":"10.1051/mmnp/2023004","DOIUrl":"https://doi.org/10.1051/mmnp/2023004","url":null,"abstract":"This work presents a model of a harvested population in a multisite environment. Locally it has the shape of the Gordon-Schaefer model. This model gives rise, placing us in the case of a fishery, to an equilibrium of the stock and the fishing effort and, therefore, of the yield that is obtained per unit of time. Considering that the management of the fishery can act on the fishing costs, the yield is optimized as a function of the cost.\u0000The objective of the work is to compare the maximum obtained yield in two extreme cases: unconnected sites and connected sites with rapid movements of both the stock and the fishing effort. The analysis of the model, first in an environment with two sites and later with any number of them, makes it possible to establish the conditions for one of the two cases to be more favorable from the point of view of the yield. In this way, it is proposed towards which of the two compared cases management should be directed.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49407569","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}
引用次数: 0
FORECAST ANALYSIS AND SLIDING MODE CONTROL ON A STOCHASTICEPIDEMIC MODEL WITH ALERTNESS AND VACCINATION 具有警戒性和疫苗接种的随机流行病模型的预测分析与滑模控制
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2023-01-18 DOI: 10.1051/mmnp/2023003
Yue Zhang, Xiju Wu
{"title":"FORECAST ANALYSIS AND SLIDING MODE CONTROL ON A STOCHASTIC\u0000\u0000EPIDEMIC MODEL WITH ALERTNESS AND VACCINATION","authors":"Yue Zhang, Xiju Wu","doi":"10.1051/mmnp/2023003","DOIUrl":"https://doi.org/10.1051/mmnp/2023003","url":null,"abstract":"In this paper, a stochastic SEIR epidemic model is studied with alertness and vaccination. The goal is to stabilize the infectious disease system quickly. The dynamic behavior of the model is analyzed and an integral sliding mode controller with distributed compensation is designed. By using Lyapunov function method, the sufficient conditions for the existence and uniqueness of global positive solutions and the existence of ergodic stationary distributions are obtained. The stochastic center manifold and stochastic average method are used to simplify the system into a one-dimensional Markov diffusion process. The stochastic stability and Hopf bifurcation are analyzed using singular boundary theory. An integral sliding mode controller with non-parallel distributed compensation is designed by linear matrix inequality (LMI) method, which realizes the stability of system and prevents the outbreak of epidemic disease. The correction of theoretical analysis and the effectiveness of controller are validated using numerical simulation performed in MATLAB/Simulink.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48606210","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}
引用次数: 0
A phenotype-structured model for the tumour-immune response 肿瘤免疫反应的表型结构模型
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2023-01-13 DOI: 10.1051/mmnp/2023025
Zineb Kaid, Camille Pouchol, Jean Clairambault Ljll, Mamba
{"title":"A phenotype-structured model for the tumour-immune response","authors":"Zineb Kaid, Camille Pouchol, Jean Clairambault Ljll, Mamba","doi":"10.1051/mmnp/2023025","DOIUrl":"https://doi.org/10.1051/mmnp/2023025","url":null,"abstract":"This paper presents a mathematical model for tumour-immune response interactions in the perspective of immunotherapy by immune checkpoint inhibitors ICIs). The model is of the nonlocal integro-differential Lotka-Volterra type, in which heterogeneity of the cell populations is taken into account by structuring variables that are continuous internal traits (aka phenotypes) present in each individual cell. These represent a lumped ``aggressiveness'', i.e., for tumour cells, malignancy understood as the ability to thrive in a viable state under attack by immune cells or drugs - which we propose to identify as a potential of de-differentiation -, and for immune cells, ability to kill tumour cells, in other words anti-tumour efficacy. We analyse the asymptotic behaviour of the model in the absence of treatment. By means of two theorems, we characterise the limits of the integro-differential system under an a priori convergence hypothesis. We illustrate our results with a few numerical simulations, which show that our model reproduces the three Es of immunoediting: elimination, equilibrium, and escape. Finally, we exemplify the possible impact of ICIs on these three Es.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46995533","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}
引用次数: 1
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