The co-infection of HIV and COVID-19 is a pressing health concern,carrying substantial potential consequences.This study focuses on the vital task of comprehending the dynamics of HIV-COVID-19 coinfection,a fundamenta...The co-infection of HIV and COVID-19 is a pressing health concern,carrying substantial potential consequences.This study focuses on the vital task of comprehending the dynamics of HIV-COVID-19 coinfection,a fundamental step in formulating efficacious control strategies and optimizing healthcare approaches.Here,we introduce an innovative mathematical model grounded in Caputo fractional order differential equations,specifically designed to encapsulate the intricate dynamics of co-infection.This model encompasses multiple critical facets:the transmission dynamics of both HIV and COVID-19,the host’s immune responses,and the influence of treatment interventions.Our approach embraces the complexity of these factors to offer an exhaustive portrayal of co-infection dynamics.To tackle the fractional order model,we employ the Laplace-Adomian decomposition method,a potent mathematical tool for approximating solutions in fractional order differential equations.Utilizing this technique,we simulate the intricate interactions between these variables,yielding profound insights into the propagation of co-infection.Notably,we identify pivotal contributors to its advancement.In addition,we conduct a meticulous analysis of the convergence properties inherent in the series solutions acquired through the Laplace-Adomian decomposition method.This examination assures the reliability and accuracy of our mathematical methodology in approximating solutions.Our findings hold significant implications for the formulation of effective control strategies.Policymakers,healthcare professionals,and public health authorities will benefit from this research as they endeavor to curtail the proliferation and impact of HIV-COVID-19 co-infection.展开更多
This paper provides a nonlinear pseudo-hyperbolic partial differential equation with non-local conditions.Despite the importance of this problem,the exact solution to this problem is rare in the literature.Therefore,t...This paper provides a nonlinear pseudo-hyperbolic partial differential equation with non-local conditions.Despite the importance of this problem,the exact solution to this problem is rare in the literature.Therefore,the Laplace-Adomian Decomposition Method(LADM)is used to provide a new approach to solving this problem.Additionally,we give a comparison between the exact and approximate solutions at various points with absolute error.The obtained result showed that the proposed method is effective and accurate for this problem and can be used for many other evolution of nonlinear equations in mathematical physics.展开更多
In this paper, we analyze a bulk input M^[X]/M/1 queue with multiple working vacations. A quasi upper triangle transition probability matrix of two-dimensional Markov chain in this model is obtained, and with the matr...In this paper, we analyze a bulk input M^[X]/M/1 queue with multiple working vacations. A quasi upper triangle transition probability matrix of two-dimensional Markov chain in this model is obtained, and with the matrix analysis method, highly complicated probability generating function（PGF） of the stationary queue length is firstly derived, from which we got the stochastic decomposition result for the stationary queue length which indicates the evident relationship with that of the classical M^[X]/M/1 queue without vacation. It is important that we find the upper and the lower bounds of the stationary waiting time in the Laplace transform order using the properties of the conditional Erlang distribution. Furthermore, we gain the mean queue length and the upper and the lower bounds of the mean waiting time.展开更多
Let be a bounded smooth domain. In this paper, the authors define the Besov spaces Bpap on , establish the atomic decomposition of these spaces, and obtain the regularity estimate of the Dirichlet problem and the Neum...Let be a bounded smooth domain. In this paper, the authors define the Besov spaces Bpap on , establish the atomic decomposition of these spaces, and obtain the regularity estimate of the Dirichlet problem and the Neumann problem for the Laplace operator on these spaces.展开更多
针对传统的基本解方法求解二维Stokes问题时,基本解矩阵病态程度高的问题,提出一个具有双重虚拟边界的基本解方法(method of fundamental solution,MFS)。基于Laplace分解,Stokes问题被转化成3个Laplace方程,进而使用具有双重虚拟边界...针对传统的基本解方法求解二维Stokes问题时,基本解矩阵病态程度高的问题,提出一个具有双重虚拟边界的基本解方法(method of fundamental solution,MFS)。基于Laplace分解,Stokes问题被转化成3个Laplace方程,进而使用具有双重虚拟边界的基本解方法求解该Laplace方程组。对应地,这3个Laplace方程的数值解被表示成源点位于2个虚拟边界上的基本解的线性组合。利用在实际边界上的边界配置点处,方程组所要满足的边界条件,得到未知系数。数值实验表明:数值解是高度准确的,与精确解相比,误差约为10-6~10-5,通过在边界上添加噪音,数值解的稳定性得到了验证;与基本解方法相比,具有双重虚拟边界的基本解方法显著地降低了基本解矩阵的条件数。展开更多
In this paper, we found the numerical solution of three-dimensional coupled Burgers’ Equations by using more efficient methods: Laplace Adomian decomposition method, Laplace transform homotopy perturbation method, va...In this paper, we found the numerical solution of three-dimensional coupled Burgers’ Equations by using more efficient methods: Laplace Adomian decomposition method, Laplace transform homotopy perturbation method, variational iteration method, variational iteration decomposition method and variational iteration homotopy perturbation method. Example is examined to validate the efficiency and accuracy of these methods and they reduce the size of computation without the restrictive assumption to handle nonlinear terms and it gives the solutions rapidly.展开更多
Herein,an approach known as conformable double Laplace decomposition method(CDLDM)is suggested for solving system of non-linear conformable fractional differential equations.The devised scheme is the combination of th...Herein,an approach known as conformable double Laplace decomposition method(CDLDM)is suggested for solving system of non-linear conformable fractional differential equations.The devised scheme is the combination of the conformable double Laplace transform method(CDLTM)and,the Adomian decomposition method(ADM).Obtained results from mathematical experiments are in full agreement with the results obtained by other methods.Furthermore,according to the results obtained we can conclude that the proposed method is efficient,reliable and easy to be implemented on related many problems in real-life science and engineering.展开更多
In this paper,we study a mathematical model of Hepatitis C Virus(HCV)infection.We present a compartmental mathematical model involving healthy hepatocytes,infected hepatocytes,non-activated dendritic cells,activated d...In this paper,we study a mathematical model of Hepatitis C Virus(HCV)infection.We present a compartmental mathematical model involving healthy hepatocytes,infected hepatocytes,non-activated dendritic cells,activated dendritic cells and cytotoxic T lymphocytes.The derivative used is of non-local fractional order and with non-singular kernel.The existence and uniqueness of the system is proven and its stability is analyzed.Then,by applying the Laplace Adomian decomposition method for the fractional derivative,we present the semi-analytical solution of the model.Finally,some numerical simulations are performed for concrete values of the parameters and several graphs are plotted to reveal the qualitative properties of the solutions.展开更多
In this research,we propose a new change in classical epidemic models by including the change in the rate of death in the overall population.The existing models like Susceptible-Infected-Recovered(SIR)and Susceptible-...In this research,we propose a new change in classical epidemic models by including the change in the rate of death in the overall population.The existing models like Susceptible-Infected-Recovered(SIR)and Susceptible-Infected-Recovered-Susceptible(SIRS)include the death rate as one of the parameters to estimate the change in susceptible,infected and recovered populations.Actually,because of the deficiencies in immunity,even the ordinary flu could cause death.If people’s disease resistance is strong,then serious diseases may not result in mortalities.The classical model always assumes a closed system where there is no new birth or death,no immigration or emigration,while in reality,such assumptions are not realistic.Moreover,the classical epidemic model does not report the change in population due to death caused by a disease.With this study,we try to incorporate the rate of change in the population of death caused by a disease,where the model is framed to reduce the curve of death along with the susceptible and infected populations.Since the rate of change turned out to be very small,we have tried to estimate it fractionally.Thus,the model is defined using fuzzy logic and is solved by two different methods:a Laplace Adomian decomposition method(LADM)and a differential transform method(DTM)for an arbitrary order α.To test its accuracy,we compared the results of both DTM and LADM with the fourth-order Runge-Kutta method(RKM-4)at α=1.展开更多
A Laplace decomposition algorithm is adopted to investigate numerical solutions of a class of nonlinear partial differential equations with nonlinear term of any order, utt ＋ auxx ＋ bu ＋ cup ＋ du^2p-1 = 0, which c...A Laplace decomposition algorithm is adopted to investigate numerical solutions of a class of nonlinear partial differential equations with nonlinear term of any order, utt ＋ auxx ＋ bu ＋ cup ＋ du^2p-1 = 0, which contains some important equations of mathematical physics. Three distinct initial conditions are constructed and generalized numerical solutions are thereby obtained, including numerical hyperbolic function solutions and doubly periodic ones. Illustrative figures and comparisons between the numerical and exact solutions with different values of p are used to test the efficiency of the proposed method, which shows good results are azhieved.展开更多
Influenza A-virus infection represents a global threat causing seasonal outbreaks andpandemics. Among the global threats creating seasonal outbreak, Influenza “A-virus”infection is a dominating theme nowadays. Using...Influenza A-virus infection represents a global threat causing seasonal outbreaks andpandemics. Among the global threats creating seasonal outbreak, Influenza “A-virus”infection is a dominating theme nowadays. Using the theory of fractional calculus, thisstudy considers an influenza model for quantitative study via the Laplace AdomianDecomposition Method (LADM). We proceed to explore the role of LADM on the proposed model. The method is described and explained for the proposed model whileproviding some plots to present the behavior of the disease.展开更多
文摘The co-infection of HIV and COVID-19 is a pressing health concern,carrying substantial potential consequences.This study focuses on the vital task of comprehending the dynamics of HIV-COVID-19 coinfection,a fundamental step in formulating efficacious control strategies and optimizing healthcare approaches.Here,we introduce an innovative mathematical model grounded in Caputo fractional order differential equations,specifically designed to encapsulate the intricate dynamics of co-infection.This model encompasses multiple critical facets:the transmission dynamics of both HIV and COVID-19,the host’s immune responses,and the influence of treatment interventions.Our approach embraces the complexity of these factors to offer an exhaustive portrayal of co-infection dynamics.To tackle the fractional order model,we employ the Laplace-Adomian decomposition method,a potent mathematical tool for approximating solutions in fractional order differential equations.Utilizing this technique,we simulate the intricate interactions between these variables,yielding profound insights into the propagation of co-infection.Notably,we identify pivotal contributors to its advancement.In addition,we conduct a meticulous analysis of the convergence properties inherent in the series solutions acquired through the Laplace-Adomian decomposition method.This examination assures the reliability and accuracy of our mathematical methodology in approximating solutions.Our findings hold significant implications for the formulation of effective control strategies.Policymakers,healthcare professionals,and public health authorities will benefit from this research as they endeavor to curtail the proliferation and impact of HIV-COVID-19 co-infection.
文摘This paper provides a nonlinear pseudo-hyperbolic partial differential equation with non-local conditions.Despite the importance of this problem,the exact solution to this problem is rare in the literature.Therefore,the Laplace-Adomian Decomposition Method(LADM)is used to provide a new approach to solving this problem.Additionally,we give a comparison between the exact and approximate solutions at various points with absolute error.The obtained result showed that the proposed method is effective and accurate for this problem and can be used for many other evolution of nonlinear equations in mathematical physics.
基金supported by National Natural Science Foundation of China(No. 10671170)Natural Science Foundation of Hebei Province(No. F2008000864)
文摘In this paper, we analyze a bulk input M^[X]/M/1 queue with multiple working vacations. A quasi upper triangle transition probability matrix of two-dimensional Markov chain in this model is obtained, and with the matrix analysis method, highly complicated probability generating function（PGF） of the stationary queue length is firstly derived, from which we got the stochastic decomposition result for the stationary queue length which indicates the evident relationship with that of the classical M^[X]/M/1 queue without vacation. It is important that we find the upper and the lower bounds of the stationary waiting time in the Laplace transform order using the properties of the conditional Erlang distribution. Furthermore, we gain the mean queue length and the upper and the lower bounds of the mean waiting time.
文摘Let be a bounded smooth domain. In this paper, the authors define the Besov spaces Bpap on , establish the atomic decomposition of these spaces, and obtain the regularity estimate of the Dirichlet problem and the Neumann problem for the Laplace operator on these spaces.
文摘针对传统的基本解方法求解二维Stokes问题时,基本解矩阵病态程度高的问题,提出一个具有双重虚拟边界的基本解方法(method of fundamental solution,MFS)。基于Laplace分解,Stokes问题被转化成3个Laplace方程,进而使用具有双重虚拟边界的基本解方法求解该Laplace方程组。对应地,这3个Laplace方程的数值解被表示成源点位于2个虚拟边界上的基本解的线性组合。利用在实际边界上的边界配置点处,方程组所要满足的边界条件,得到未知系数。数值实验表明:数值解是高度准确的,与精确解相比,误差约为10-6~10-5,通过在边界上添加噪音,数值解的稳定性得到了验证;与基本解方法相比,具有双重虚拟边界的基本解方法显著地降低了基本解矩阵的条件数。
文摘In this paper, we found the numerical solution of three-dimensional coupled Burgers’ Equations by using more efficient methods: Laplace Adomian decomposition method, Laplace transform homotopy perturbation method, variational iteration method, variational iteration decomposition method and variational iteration homotopy perturbation method. Example is examined to validate the efficiency and accuracy of these methods and they reduce the size of computation without the restrictive assumption to handle nonlinear terms and it gives the solutions rapidly.
文摘Herein,an approach known as conformable double Laplace decomposition method(CDLDM)is suggested for solving system of non-linear conformable fractional differential equations.The devised scheme is the combination of the conformable double Laplace transform method(CDLTM)and,the Adomian decomposition method(ADM).Obtained results from mathematical experiments are in full agreement with the results obtained by other methods.Furthermore,according to the results obtained we can conclude that the proposed method is efficient,reliable and easy to be implemented on related many problems in real-life science and engineering.
基金supported by the Agencia Estatal de Investigacin(AEI)of Spain,co-financed by the European Fund for Regional Development(FEDER)corresponding to the 2014-2020 multiyear financial framework,project PID2020-113275GB-I00Instituto de Salud Carlos II,grant COV20/00617Xunta de Galicia under grant ED431C 2019/02.
文摘In this paper,we study a mathematical model of Hepatitis C Virus(HCV)infection.We present a compartmental mathematical model involving healthy hepatocytes,infected hepatocytes,non-activated dendritic cells,activated dendritic cells and cytotoxic T lymphocytes.The derivative used is of non-local fractional order and with non-singular kernel.The existence and uniqueness of the system is proven and its stability is analyzed.Then,by applying the Laplace Adomian decomposition method for the fractional derivative,we present the semi-analytical solution of the model.Finally,some numerical simulations are performed for concrete values of the parameters and several graphs are plotted to reveal the qualitative properties of the solutions.
文摘In this research,we propose a new change in classical epidemic models by including the change in the rate of death in the overall population.The existing models like Susceptible-Infected-Recovered(SIR)and Susceptible-Infected-Recovered-Susceptible(SIRS)include the death rate as one of the parameters to estimate the change in susceptible,infected and recovered populations.Actually,because of the deficiencies in immunity,even the ordinary flu could cause death.If people’s disease resistance is strong,then serious diseases may not result in mortalities.The classical model always assumes a closed system where there is no new birth or death,no immigration or emigration,while in reality,such assumptions are not realistic.Moreover,the classical epidemic model does not report the change in population due to death caused by a disease.With this study,we try to incorporate the rate of change in the population of death caused by a disease,where the model is framed to reduce the curve of death along with the susceptible and infected populations.Since the rate of change turned out to be very small,we have tried to estimate it fractionally.Thus,the model is defined using fuzzy logic and is solved by two different methods:a Laplace Adomian decomposition method(LADM)and a differential transform method(DTM)for an arbitrary order α.To test its accuracy,we compared the results of both DTM and LADM with the fourth-order Runge-Kutta method(RKM-4)at α=1.
基金Supported by National Natural Science Foundation of China under Grant No.11301269,and 11301266Jiangsu Provincial Natural Science Foundation of China under Grant No.BK20130665the Fundamental Research Funds KJ2013036 for the Central Universities
文摘A Laplace decomposition algorithm is adopted to investigate numerical solutions of a class of nonlinear partial differential equations with nonlinear term of any order, utt ＋ auxx ＋ bu ＋ cup ＋ du^2p-1 = 0, which contains some important equations of mathematical physics. Three distinct initial conditions are constructed and generalized numerical solutions are thereby obtained, including numerical hyperbolic function solutions and doubly periodic ones. Illustrative figures and comparisons between the numerical and exact solutions with different values of p are used to test the efficiency of the proposed method, which shows good results are azhieved.
文摘Influenza A-virus infection represents a global threat causing seasonal outbreaks andpandemics. Among the global threats creating seasonal outbreak, Influenza “A-virus”infection is a dominating theme nowadays. Using the theory of fractional calculus, thisstudy considers an influenza model for quantitative study via the Laplace AdomianDecomposition Method (LADM). We proceed to explore the role of LADM on the proposed model. The method is described and explained for the proposed model whileproviding some plots to present the behavior of the disease.
