The present paper deals with the periodic behaviours of an age-structured populationmodel.The period-similarity is proposed,which reveals a certain similar structure between thosepopulation models with distinct age st...The present paper deals with the periodic behaviours of an age-structured populationmodel.The period-similarity is proposed,which reveals a certain similar structure between thosepopulation models with distinct age structure.In addition,other results show that the fluctuations ofan age-structured population are closely related with the age structure.展开更多
This paper presents a novel analysis for the solution of nonlinear age-structured prob- lem which is of extreme importance in biological sciences. The presented model is very useful but quite complicated. Modified var...This paper presents a novel analysis for the solution of nonlinear age-structured prob- lem which is of extreme importance in biological sciences. The presented model is very useful but quite complicated. Modified variational iteration method （MVIM） coupled with auxiliary parameter is used to cope with the complexity of the model which subse- quently shows better results as compared to some existing results available in literature. Furthermore, an appropriate way is used for the identification of auxiliary parameter by means of residual function. Numerical examples are presented for the analysis of the pro- posed algorithm. Graphical results along with the discussions re-confirm the efficiency of proposed algorithm. The work proposes a new algorithm where He＇s polynomials and an auxiliary parameter are merged with correction functional. The suggested scheme is implemented on nonlinear age-structured population models. Graphs are plotted for the residual function that reflects the accuracy and convergence of the presented algorithm.展开更多
In this study, Haar wavelet method is implemented for solving the nonlinear age- structured population model which is the nonclassic type of partial differential equation associated with boundary integral equation. Th...In this study, Haar wavelet method is implemented for solving the nonlinear age- structured population model which is the nonclassic type of partial differential equation associated with boundary integral equation. This paper develops the flexibility of Haar wavelet method for reduction of the partial differential equation with nonlocal boundary conditions to an algebraic system. In fact, the simple structure of piecewise orthogonM Haar basis functions which leads to sparse matrices causes the convergence and com- putational efficiency. Some illustrative results show the reliability and accuracy of the presented method.展开更多
This article focuses on the study of an age structured SEIRS epidemic model with a vaccination program when the total population size is not kept at constant. We first give the explicit expression of the reproduction ...This article focuses on the study of an age structured SEIRS epidemic model with a vaccination program when the total population size is not kept at constant. We first give the explicit expression of the reproduction number in the presence of vaccine ( is the exponent of growth of total population), and show that the infection-free steady state is linearly stable if and unstable if , then we apply the theoretical results to vaccination policies to determine the optimal age or ages at which an individual should be vaccinated. It is shown that the optimal strategy can be either one- or two-age strategies.展开更多
Three analytic algorithms based on Adomian decomposition, homotopy perturbation and homotopy analysis methods are proposed to solve some models of nonlinear age-structured population dynamics and epidemiology. Truncat...Three analytic algorithms based on Adomian decomposition, homotopy perturbation and homotopy analysis methods are proposed to solve some models of nonlinear age-structured population dynamics and epidemiology. Truncating the resulting convergent infinite series, we obtain numerical solutions of high accuracy for these models. Three numerical examples are given to illustrate the simplicity and accuracy of the methods.展开更多
文摘The present paper deals with the periodic behaviours of an age-structured populationmodel.The period-similarity is proposed,which reveals a certain similar structure between thosepopulation models with distinct age structure.In addition,other results show that the fluctuations ofan age-structured population are closely related with the age structure.
文摘This paper presents a novel analysis for the solution of nonlinear age-structured prob- lem which is of extreme importance in biological sciences. The presented model is very useful but quite complicated. Modified variational iteration method （MVIM） coupled with auxiliary parameter is used to cope with the complexity of the model which subse- quently shows better results as compared to some existing results available in literature. Furthermore, an appropriate way is used for the identification of auxiliary parameter by means of residual function. Numerical examples are presented for the analysis of the pro- posed algorithm. Graphical results along with the discussions re-confirm the efficiency of proposed algorithm. The work proposes a new algorithm where He＇s polynomials and an auxiliary parameter are merged with correction functional. The suggested scheme is implemented on nonlinear age-structured population models. Graphs are plotted for the residual function that reflects the accuracy and convergence of the presented algorithm.
文摘In this study, Haar wavelet method is implemented for solving the nonlinear age- structured population model which is the nonclassic type of partial differential equation associated with boundary integral equation. This paper develops the flexibility of Haar wavelet method for reduction of the partial differential equation with nonlocal boundary conditions to an algebraic system. In fact, the simple structure of piecewise orthogonM Haar basis functions which leads to sparse matrices causes the convergence and com- putational efficiency. Some illustrative results show the reliability and accuracy of the presented method.
基金Supported by the NSFC (No.10371105) and the NSF of Henan Province (No.0312002000No.0211044800)
文摘This article focuses on the study of an age structured SEIRS epidemic model with a vaccination program when the total population size is not kept at constant. We first give the explicit expression of the reproduction number in the presence of vaccine ( is the exponent of growth of total population), and show that the infection-free steady state is linearly stable if and unstable if , then we apply the theoretical results to vaccination policies to determine the optimal age or ages at which an individual should be vaccinated. It is shown that the optimal strategy can be either one- or two-age strategies.
文摘Three analytic algorithms based on Adomian decomposition, homotopy perturbation and homotopy analysis methods are proposed to solve some models of nonlinear age-structured population dynamics and epidemiology. Truncating the resulting convergent infinite series, we obtain numerical solutions of high accuracy for these models. Three numerical examples are given to illustrate the simplicity and accuracy of the methods.
