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Malaria and cholera co-dynamic model analysis furnished with fractional-order differential equations 基于分数阶微分方程的疟疾和霍乱共动力模型分析
Mathematical Modelling and Numerical Simulation with Applications Pub Date : 2023-03-31 DOI: 10.53391/mmnsa.1273982
Livinus L. Iwa, U. K. Nwajeri, A. O. Atede, A. B. Panle, K. U. Egeonu
{"title":"Malaria and cholera co-dynamic model analysis furnished with fractional-order differential equations","authors":"Livinus L. Iwa, U. K. Nwajeri, A. O. Atede, A. B. Panle, K. U. Egeonu","doi":"10.53391/mmnsa.1273982","DOIUrl":"https://doi.org/10.53391/mmnsa.1273982","url":null,"abstract":"This paper presents malaria and cholera co-dynamics under Caputo-Fabrizio derivative of order $alphain(0,1)$ varied with some notable parameters in the fractional system. The fractional order system comprises ten compartments divided into human and vector classes. The human population is exposed to obnoxious diseases such as malaria and cholera which can lead to an untimely death if proper care is not taken. As a result, we present the qualitative analysis of the fractional order system where the existence and uniqueness of the solution using the well-known Banach and Schauder fixed point theorems. The numerical solution of the system is achieved through the famous iterative Atangana-Baleanu fractional order Adams-Bashforth scheme. The numerical algorithm obtained from the scheme is used for graphic simulation for different fractional orders $alphain (0,1)$. The figures produced using various fractional orders show total convergence and stability as time increases. It is also evident that stability and convergence are achieved as the fractional orders tend to 1. The actual behavior of the fractional co-dynamical system of the diseases is established also in the numerical simulation.","PeriodicalId":210715,"journal":{"name":"Mathematical Modelling and Numerical Simulation with Applications","volume":"115 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132672643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
A modelling of bioconvective flow existing with tiny particles and quartic autocatalysis reaction across stratified upper horizontal surface of a paraboloid of revolution 微小颗粒和四次自催化反应存在于旋转抛物面分层上水平面上的生物对流流动模型
Mathematical Modelling and Numerical Simulation with Applications Pub Date : 2023-03-31 DOI: 10.53391/mmnsa.1280184
Nehad Ali Shah, A. Popoola, T. Oreyeni, E. Omokhuale, M. Altine
{"title":"A modelling of bioconvective flow existing with tiny particles and quartic autocatalysis reaction across stratified upper horizontal surface of a paraboloid of revolution","authors":"Nehad Ali Shah, A. Popoola, T. Oreyeni, E. Omokhuale, M. Altine","doi":"10.53391/mmnsa.1280184","DOIUrl":"https://doi.org/10.53391/mmnsa.1280184","url":null,"abstract":"The study considers the case of the unequal diffusion coefficients of reactant $A$ (bulk fluid) and reactant $B$ (catalyst at the wall) with the dispersion of both nanoparticles and gyrotactic microorganisms of Erying-Powell fluid flow over a surface with non-uniform thickness in the presence of variable fluid properties and stratification. The numerical solution of the transformed governing equations is obtained by using the Runge-Kutta method and shooting techniques. The outcome of this study is that the increasing values of temperature-dependent thermal conductivity parameter lead to the augmentation of the kinetic energy which thereafter causes a significant enhancement of the fluid temperature.","PeriodicalId":210715,"journal":{"name":"Mathematical Modelling and Numerical Simulation with Applications","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128138853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Finite volume simulation of calcium distribution in a cholangiocyte cell 胆管细胞内钙分布的有限体积模拟
Mathematical Modelling and Numerical Simulation with Applications Pub Date : 2023-03-31 DOI: 10.53391/mmnsa.1273945
Nakul Nakul, Vedika Mishra, N. Adlakha
{"title":"Finite volume simulation of calcium distribution in a cholangiocyte cell","authors":"Nakul Nakul, Vedika Mishra, N. Adlakha","doi":"10.53391/mmnsa.1273945","DOIUrl":"https://doi.org/10.53391/mmnsa.1273945","url":null,"abstract":"Cholangiocytes are the cells of the liver having a major role in the conditioning of bile used in digestion. Other functions of cholangiocytes are in apoptosis and bicarbonate secretion. The Calcium in the intracellular environment of various cells including cholangiocytes regulates a large number of functions. This regulating mechanism in cholangiocytes has been poorly understood to date. In order to analyze the calcium regulation in cholangiocyte cells, a mathematical model for a one-dimensional steady-state case is constructed in this study. This involves a non-linear reaction-diffusion equation with appropriate boundary conditions. The influx from IP$_{3}$ receptor, ryanodine receptor (RYR), and plasma membrane as well as the efflux of calcium from SERCA pump and plasma membrane have been employed in the model. The finite volume method and Newton-Raphson method have been used to solve the problem. Numerical findings have been used to examine the effects of parameters like diffusion coefficient, rate of SERCA pump efflux, buffer, and influx from plasma membrane on calcium concentration in cholangiocyte cells. The information generated from the model can be useful for understanding the mechanism of cholestatic disorders which can be further useful in the diagnosis and treatment of these disorders.","PeriodicalId":210715,"journal":{"name":"Mathematical Modelling and Numerical Simulation with Applications","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115368734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Mathematical modelling of a glucose-insulin system for type 2 diabetic patients in Chad 乍得2型糖尿病患者葡萄糖-胰岛素系统的数学建模
Mathematical Modelling and Numerical Simulation with Applications Pub Date : 2022-12-30 DOI: 10.53391/mmnsa.2022.020
Adam Hassan Adoum, M. Haggar, J. Ntaganda
{"title":"Mathematical modelling of a glucose-insulin system for type 2 diabetic patients in Chad","authors":"Adam Hassan Adoum, M. Haggar, J. Ntaganda","doi":"10.53391/mmnsa.2022.020","DOIUrl":"https://doi.org/10.53391/mmnsa.2022.020","url":null,"abstract":"In this paper, we focus on modelling the glucose-insulin system for the purpose of estimating glucagon, insulin, and glucose in the liver in the internal organs of the human body. A three-compartmental mathematical model is proposed. The model parameters are estimated using a nonlinear inverse optimization problem and data collected in Chad. In order to identify insulin and glucose in the liver for type 2 diabetic patients, the Sampling Importance Resampling (SIR) particle filtering algorithm is used and implemented through discretization of the developed mathematical model. The proposed mathematical model allows further investigation of the dynamic behavior of hepatic glucose, insulin, and glucagon in internal organs for type 2 diabetic patients. During periods of hyperglycemia (i.e., after meal ingestion), whereas insulin secretion is increased, glucagon secretion is reduced. The results are in agreement with empirical and clinical data and they are clinically consistent with physiological responses.","PeriodicalId":210715,"journal":{"name":"Mathematical Modelling and Numerical Simulation with Applications","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121004001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Dynamics of a fractional-order COVID-19 model under the nonsingular kernel of Caputo-Fabrizio operator Caputo-Fabrizio算子非奇异核下分数阶COVID-19模型的动力学
Mathematical Modelling and Numerical Simulation with Applications Pub Date : 2022-12-29 DOI: 10.53391/mmnsa.2022.019
Saeed Ahmad, D. Qiu, Mati ur Rahman
{"title":"Dynamics of a fractional-order COVID-19 model under the nonsingular kernel of Caputo-Fabrizio operator","authors":"Saeed Ahmad, D. Qiu, Mati ur Rahman","doi":"10.53391/mmnsa.2022.019","DOIUrl":"https://doi.org/10.53391/mmnsa.2022.019","url":null,"abstract":"For the sake of human health, it is crucial to investigate infectious diseases including HIV/AIDS, hepatitis, and others. Worldwide, the recently discovered new coronavirus (COVID-19) poses a serious threat. The experimental vaccination and different COVID-19 strains found around the world make the virus' spread unavoidable. In the current research, fractional order is used to study the dynamics of a nonlinear modified COVID-19 SEIR model in the framework of the Caputo-Fabrizio fractional operator with order b. Fixed point theory has been used to investigate the qualitative analysis of the solution respectively. The well-known Laplace transform method is used to determine the approximate solution of the proposed model. Using the COVID-19 data that is currently available, numerical simulations are run to validate the necessary scheme and examine the dynamic behavior of the various compartments of the model. In order to stop the pandemic from spreading, our findings highlight the significance of taking preventative steps and changing one's lifestyle.","PeriodicalId":210715,"journal":{"name":"Mathematical Modelling and Numerical Simulation with Applications","volume":"237 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116776389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 18
On the relations between a singular system of differential equations and a system with delays 关于奇异微分方程组与时滞系统的关系
Mathematical Modelling and Numerical Simulation with Applications Pub Date : 2022-12-28 DOI: 10.53391/mmnsa.2022.018
I. Dassios
{"title":"On the relations between a singular system of differential equations and a system with delays","authors":"I. Dassios","doi":"10.53391/mmnsa.2022.018","DOIUrl":"https://doi.org/10.53391/mmnsa.2022.018","url":null,"abstract":"In this article, we consider a class of systems of differential equations with multiple delays. We define a transform that reformulates the system with delays into a singular linear system of differential equations whose coefficients are non-square constant matrices, and the number of their columns is greater than the number of their rows. By studying only the singular system, we provide a form of solutions for both systems.","PeriodicalId":210715,"journal":{"name":"Mathematical Modelling and Numerical Simulation with Applications","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133042374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
A new analytical approach to the (1+1)-dimensional conformable Fisher equation (1+1)维适形费雪方程的一种新的解析方法
Mathematical Modelling and Numerical Simulation with Applications Pub Date : 2022-12-27 DOI: 10.53391/mmnsa.2022.017
Gulnur Yel, M. Kayhan, A. Ciancio
{"title":"A new analytical approach to the (1+1)-dimensional conformable Fisher equation","authors":"Gulnur Yel, M. Kayhan, A. Ciancio","doi":"10.53391/mmnsa.2022.017","DOIUrl":"https://doi.org/10.53391/mmnsa.2022.017","url":null,"abstract":"In this paper, we use an effective method which is the rational sine-Gordon expansion method to present new wave simulations of a governing model. We consider the (1+1)-dimensional conformable Fisher equation which is used to describe the interactive relation between diffusion and reaction. Various types of solutions such as multi-soliton, kink, and anti-kink wave soliton solutions are obtained. Finally, the physical behaviours of the obtained solutions are shown by 3D, 2D, and contour surfaces.","PeriodicalId":210715,"journal":{"name":"Mathematical Modelling and Numerical Simulation with Applications","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126056207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Set-valued analysis of anti-angiogenic therapy and radiotherapy 抗血管生成治疗与放疗的集值分析
Mathematical Modelling and Numerical Simulation with Applications Pub Date : 2022-09-29 DOI: 10.53391/mmnsa.2022.015
Amine Moustafid
{"title":"Set-valued analysis of anti-angiogenic therapy and radiotherapy","authors":"Amine Moustafid","doi":"10.53391/mmnsa.2022.015","DOIUrl":"https://doi.org/10.53391/mmnsa.2022.015","url":null,"abstract":"The aim of the paper is to study a cancer model based on anti-angiogenic therapy and radiotherapy. A set-valued analysis is carried out to control the tumor and carrying capacity of the vasculature, so in order to reverse tumor growth and augment tumor repair. The viability technique is used on an augmented model to solve the control problem. Obtained control is a selection of set-valued map of regulation and reduces tumor volume to around zero. A numerical simulation scheme with graphical representations and biological interpretations are given.","PeriodicalId":210715,"journal":{"name":"Mathematical Modelling and Numerical Simulation with Applications","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124983477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Laplace transform collocation method for telegraph equations defined by Caputo derivative 由卡普托导数定义的电报方程的拉普拉斯变换配点法
Mathematical Modelling and Numerical Simulation with Applications Pub Date : 2022-09-28 DOI: 10.53391/mmnsa.2022.014
Mahmut Modanlı, M. E. Koksal
{"title":"Laplace transform collocation method for telegraph equations defined by Caputo derivative","authors":"Mahmut Modanlı, M. E. Koksal","doi":"10.53391/mmnsa.2022.014","DOIUrl":"https://doi.org/10.53391/mmnsa.2022.014","url":null,"abstract":"The purpose of this paper is to find approximate solutions to the fractional telegraph differential equation (FTDE) using Laplace transform collocation method (LTCM). The equation is defined by Caputo fractional derivative. A new form of the trial function from the original equation is presented and unknown coefficients in the trial function are computed by using LTCM. Two different initial-boundary value problems are considered as the test problems and approximate solutions are compared with analytical solutions. Numerical results are presented by graphs and tables. From the obtained results, we observe that the method is accurate, effective, and useful.","PeriodicalId":210715,"journal":{"name":"Mathematical Modelling and Numerical Simulation with Applications","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123645638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Stability characterization of a fractional-order viral system with the non-cytolytic immune assumption 分数阶病毒系统在非细胞溶解性免疫假设下的稳定性表征
Mathematical Modelling and Numerical Simulation with Applications Pub Date : 2022-09-25 DOI: 10.53391/mmnsa.2022.013
M. Naim, Y. Sabbar, A. Zeb
{"title":"Stability characterization of a fractional-order viral system with the non-cytolytic immune assumption","authors":"M. Naim, Y. Sabbar, A. Zeb","doi":"10.53391/mmnsa.2022.013","DOIUrl":"https://doi.org/10.53391/mmnsa.2022.013","url":null,"abstract":"This article deals with a Caputo fractional-order viral model that incorporates the non-cytolytic immune hypothesis and the mechanism of viral replication inhibition. Firstly, we establish the existence, uniqueness, non-negativity, and boundedness of the solutions of the proposed viral model. Then, we point out that our model has the following three equilibrium points: equilibrium point without virus, equilibrium state without immune system, and equilibrium point activated by immunity with humoral feedback. By presenting two critical quantities, the asymptotic stability of all said steady points is examined. Finally, we examine the finesse of our results by highlighting the impact of fractional derivatives on the stability of the corresponding steady points.","PeriodicalId":210715,"journal":{"name":"Mathematical Modelling and Numerical Simulation with Applications","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134183736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 22
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