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Investigation of COVID-19 Mathematical Model Under Fractional Order Derivative 分数阶导数下新冠肺炎数学模型的研究
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2021-08-24 DOI: 10.1051/mmnp/2021044
K. Shah, M. Arfan, Meshal Shutaywi, Wejdan Deebani, Dumitru Balaneau
{"title":"Investigation of COVID-19 Mathematical Model Under Fractional Order Derivative","authors":"K. Shah, M. Arfan, Meshal Shutaywi, Wejdan Deebani, Dumitru Balaneau","doi":"10.1051/mmnp/2021044","DOIUrl":"https://doi.org/10.1051/mmnp/2021044","url":null,"abstract":"The given article is devoted to presentation of some results regarding existence and uniqueness of solution to a fractional order model that addressing the effect of immigration on the transmission dynamics of a population model. Further, in view of this investigation the effect of immigration have been checked on transmission of recent pandemic known as Corona virus COVID-19. The concerned results have been established by using fixed point theory approach. After investigation qualitative analysis of the considered model, by applying Laplace transform along with decomposition method, we have calculated some series type results for the concerned model. The unknown quantities of each equation have been decomposed into small quantities to calculate each small quantity very easily for the series solution by adding first few terms of the said quantities. Approximate results of some testing data with different cases are given to illustrate the results.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42301673","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
Invariant measure of stochastic higher order KdV equation driven by Poisson processes 泊松过程驱动的随机高阶KdV方程的不变测度
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2021-08-23 DOI: 10.1051/MMNP/2021041
Pengfei Xu, Jianhua Huang, Wei Yan
{"title":"Invariant measure of stochastic higher order KdV equation driven by Poisson processes","authors":"Pengfei Xu, Jianhua Huang, Wei Yan","doi":"10.1051/MMNP/2021041","DOIUrl":"https://doi.org/10.1051/MMNP/2021041","url":null,"abstract":"The current paper is devoted to stochastic damped higher order KdV equation driven by Poisson process. We establish the well-posedness of stochastic damped higher-order KdV equation, and prove that there exists an unique invariant measure for non-random initial conditions. Some discussion on the general pure jump noise case are also provided. Some numerical simulations of the invariant measure are provided to support the theoretical results. Mathematics Subject Classification. 60H15, 37L55. Received March 27, 2020. Accepted July 13, 2021.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43425632","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: 2
Spatiotemporal pattern formation in a prey-predator model with generalist predator 具有通才捕食者的捕食-捕食模型的时空格局形成
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2021-07-03 DOI: 10.22541/AU.162531612.21576519/V1
Kalyan Manna, M. Banerjee
{"title":"Spatiotemporal pattern formation in a prey-predator model with generalist predator","authors":"Kalyan Manna, M. Banerjee","doi":"10.22541/AU.162531612.21576519/V1","DOIUrl":"https://doi.org/10.22541/AU.162531612.21576519/V1","url":null,"abstract":"Generalist predators exploit multiple food sources and it is economical\u0000for them to reduce predation pressure on a particular prey species when\u0000their density level becomes comparatively less. As a result, a\u0000prey-predator system tends to become more stable in the presence of a\u0000generalist predator. In this article, we investigate the roles of both\u0000the diffusion and nonlocal prey consumption in shaping the population\u0000distributions for interacting generalist predator and its focal prey\u0000species. In this regard, we first derive the conditions associated with\u0000Turing instability through linear analysis. Then, we perform a weakly\u0000nonlinear analysis and derive a cubic Stuart-Landau equation governing\u0000amplitude of the resulting patterns near Turing bifurcation boundary.\u0000Further, we present a wide variety of numerical simulations to\u0000corroborate our analytical findings as well as to illustrate some other\u0000complex spatiotemporal dynamics. Interestingly, our study reveals the\u0000existence of traveling wave solutions connecting two spatially\u0000homogeneous coexistence steady states in Turing domain under the\u0000influence of temporal bistability phenomenon. Also, our investigation\u0000shows that nonlocal prey consumption acts as a stabilizing force for the\u0000system dynamics.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":"33 22","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41308462","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: 4
Numerical simulation of rigid particles in Stokes flow: lubrication correction for general shapes of particles Stokes流中刚性粒子的数值模拟：对一般形状粒子的润滑修正
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2021-06-28 DOI: 10.1051/MMNP/2021037
A. Lefebvre-Lepot, Flore Nabet
{"title":"Numerical simulation of rigid particles in Stokes flow: lubrication correction for general shapes of particles","authors":"A. Lefebvre-Lepot, Flore Nabet","doi":"10.1051/MMNP/2021037","DOIUrl":"https://doi.org/10.1051/MMNP/2021037","url":null,"abstract":"We address the problem of numerical simulation of suspensions of rigid particles in a Stokes flow. We focus on the inclusion of the singular short range interaction effects (lubrication effects) in the simulations when the particles come close one to another. The problem is solved without introducing new hypothesis nor model. As in Lefebvre-Lepot et al. [J. Fluid Mech. 769 (2015) 369–386], the key idea is to decompose the velocity and pressure flows in a sum of a singular and a regular part. In this article, the singular part is computed using an explicit asymptotic expansion of the solution when the distance goes to zero. This expansion is similar to the asymptotic expansion proposed in Hillairet and Kelai [Asymptotic Anal. 95 (2015) 187–241] but is more appropriate for numerical simulations of suspensions. It can be computed for any locally convex (that is the particles have to be convex close to the contact point) and regular shape of particles. Using Hillairet and Kelai [Asymptotic Anal. 95 (2015) 187–241] as an intermediate result, we prove that the remaining part is regular in the sense that it is bounded independently of the distance. As a consequence, only a small number of degrees of freedom are necessary to obtain accurate results. The method is tested in dimension 2 for clusters of two or three aligned particles with general rigid velocities. We show that, as expected, the convergence is independent of the distance.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43714941","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
Dynamics and control of loop reactors - a review 循环反应器的动力学与控制综述
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2021-06-14 DOI: 10.1051/MMNP/2021035
M. Sheintuch, O. Nekhamkina
{"title":"Dynamics and control of loop reactors - a review","authors":"M. Sheintuch, O. Nekhamkina","doi":"10.1051/MMNP/2021035","DOIUrl":"https://doi.org/10.1051/MMNP/2021035","url":null,"abstract":"In loop reactors the system is composed of several reactor units that are  organized in a loop and the feeding takes place at one of several ports with switching of the feed port. In its simplest operation a pulse is formed and rotates around it, producing high temperatures which enable combustion of dilute streams.  A limiting model with infinite number of units was derived. Rotating pulses, steady in a moving coordinate, emerge in both models when the switching to front propagation velocities ~1. But this behavior exists over a narrow domain. Simulations were conducted with generic first order Arrhenius kinetics. Experimental observations are reviewed.\u0000Outside the narrow frozen rotating pattern domain the system may exhibit multi- or quasi-periodic operation separated by domains of inactive reaction. The bifurcation set incorporates many 'finger'-like domains of complex frequency-locked solutions that allow to extend the operation domain with higher feed temperatures.\u0000Control is necessary to attain stable simple rotating frozen pattern within the narrow domains of active operation. Various tested control approaches are reviewed.\u0000         Actual implementation of combustion in LR will involve several reactants of different ignition temperatures. Design and control should be aimed at producing locked fronts and avoid extinction of slower reactions.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46721160","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
Effects of Heterogeneity and Global Dynamics of Weakly Connected Subpopulations 弱连接亚居群的异质性和全局动态效应
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2021-06-14 DOI: 10.1051/MMNP/2021034
Derdei Bichara, A. Iggidr, Souâd Yacheur
{"title":"Effects of Heterogeneity and Global Dynamics of Weakly Connected Subpopulations","authors":"Derdei Bichara, A. Iggidr, Souâd Yacheur","doi":"10.1051/MMNP/2021034","DOIUrl":"https://doi.org/10.1051/MMNP/2021034","url":null,"abstract":"We develop a method that completely characterizes the global dynamics of models with multiple subpopulations that are weakly interconnected. The method is applied on two classes of models with multiple subpopulations: an epidemic model that involves multiple host species and multiple vector species and a patchy vector-borne model. The method consists of two main steps: reducing the system using tools of large scale systems and studying the dynamics of an auxiliary system related the original system. The developed method determines the underlying dynamics and the ``weight\" of each subpopulations with respect to the dynamics of the whole population, and how the topology of the connectivity matrix alters the dynamics of the overall population. The method provides global stability results for all types of equilibria, namely trivial, boundary or interior equilibria.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46951992","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: 2
Three-dimensional phase field model for actin-based cell membrane dynamics 基于肌动蛋白的细胞膜动力学三维相场模型
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2021-06-03 DOI: 10.1051/mmnp/2021048
M. Hamed, A. Nepomnyashchy
{"title":"Three-dimensional phase field model for actin-based cell membrane dynamics","authors":"M. Hamed, A. Nepomnyashchy","doi":"10.1051/mmnp/2021048","DOIUrl":"https://doi.org/10.1051/mmnp/2021048","url":null,"abstract":"The interface dynamics of a 3D cell immersed in a 3D extracellular matrix is investigated. We suggest a 3D generalization of a known 2D minimal phase field model suggested in Ziebert et al. [J. R. Soc. Interface 9 (2012) 1084–1092] for the description of keratocyte motility. Our model consists of two coupled evolution equations for the order parameter and a three-dimensional vector field describing the actin network polarization (orientation). We derive a closed evolutionary integro-differential equation governing the interface dynamics of a 3D cell. The equation includes the normal velocity of the membrane, its curvature, cell volume relaxation, and a parameter that is determined by the non-equilibrium effects in the cytoskeleton. This equation can be considered as a 3D generalization of the 2D case that was studied in Abu Hamed and Nepomnyashchy [Physica D 408 (2020)].","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47229551","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: 3
A stability theorem for equilibria of delay differential equations in a critical case with application to a model of cell evolution 临界情况下时滞微分方程平衡点的稳定性定理及其在细胞进化模型中的应用
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2021-05-04 DOI: 10.1051/MMNP/2021021
karim O. Amin, Irina Badralexi, A. Halanay, R. Mghames
{"title":"A stability theorem for equilibria of delay differential equations in a critical case with application to a model of cell evolution","authors":"karim O. Amin, Irina Badralexi, A. Halanay, R. Mghames","doi":"10.1051/MMNP/2021021","DOIUrl":"https://doi.org/10.1051/MMNP/2021021","url":null,"abstract":"In this paper the stability of the zero equilibrium of a system with time delay is studied. The critical case of a multiple zero root of the characteristic equation of the linearized system is treated by applying a Malkin type theorem and using a complete Lyapunov-Krasovskii functional. An application to a model for malaria under treatment considering the action of the immune system is presented.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42817527","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: 3
SIARD model and effect of lockdown on the dynamics of COVID-19 disease with non total immunity SIARD模型及封锁对非完全免疫COVID-19疾病动力学的影响
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2021-04-28 DOI: 10.1051/MMNP/2021025
M. Aziz-Alaoui, F. Najm, R. Yafia
{"title":"SIARD model and effect of lockdown on the dynamics of COVID-19 disease with non total immunity","authors":"M. Aziz-Alaoui, F. Najm, R. Yafia","doi":"10.1051/MMNP/2021025","DOIUrl":"https://doi.org/10.1051/MMNP/2021025","url":null,"abstract":"We propose a new compartmental mathematical model describing the transmission and the spreading of COVID-19 epidemic with a special focus on the non-total immunity. The model (called SIARD) is given by a system of differential equations which model the interactions between five populations “susceptible”, “reported infectious”, “unreported infectious”, “recovered with/without non total immunity” and “death”. Depending on the basic reproduction number, we prove that the total immunity induces local stability-instability of equilibria and the epidemic may disappear after a first epidemic wave and more epidemic waves may appear in the case of non-total immunity. Using the sensitivity analysis we identify the most sensitive parameters. Numerical simulations are carried out to illustrate our theoretical results. As an application, we found that our model fits well the Moroccan epidemic wave, and predicts more than one wave for French case.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48279215","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: 5
Within-host evolutionary dynamics of antimicrobial quantitative resistance 宿主内抗菌素数量耐药性的进化动力学
IF 2.2 4区 数学
Mathematical Modelling of Natural Phenomena Pub Date : 2021-04-09 DOI: 10.1051/mmnp/2023019
R. Djidjou-Demasse, M. Sofonea, Marc Choisy, Samuel Alizon, R. Djidjou-Demassea, Mircea T. Sofoneaa
{"title":"Within-host evolutionary dynamics of antimicrobial quantitative resistance","authors":"R. Djidjou-Demasse, M. Sofonea, Marc Choisy, Samuel Alizon, R. Djidjou-Demassea, Mircea T. Sofoneaa","doi":"10.1051/mmnp/2023019","DOIUrl":"https://doi.org/10.1051/mmnp/2023019","url":null,"abstract":"10 Antimicrobial efficacy is traditionally described by a single value, the minimal inhibitory concentration (MIC), which is the lowest concentration that prevents visible growth of the bacterial population. As a consequence, bacteria are classically qualitatively categorized as resistant if therapeutic concentrations are below MIC and susceptible otherwise. However, there is a continuity in the space of the bacterial resistance levels. Here, we introduce a model of within-host evolution","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43457550","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: 2
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