具有垂直传播和时间周期的登革热模型的三次B样条拟插值法数值解  

Numerical Solutions of the Dengue Fever Model with Vertical Propagation and Time Period via Cubic B-spline Quasi-interpolation

作　　者：钱江[1] 陈雨青 QIAN Jiang;CHEN Yuqing(College of Science,Hohai University,Nanjing 211100)

机构地区：[1]河海大学理学院,南京211100

出　　处：《工程数学学报》2023年第2期281-294,共14页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11601151);海岸灾害与防护教育部重点实验室开放基金(202011);江苏省自然科学基金(BK20160853);河海大学中央高校基本科研业务费(2016B08714,2019B19414).

摘　　要：数学模型是理解和控制传染病传播的重要途径。利用三次B样条拟插值法求解一类具有垂直传播和时间周期的登革热数学模型,首先介绍三次B样条拟插值的基本知识,接着用拟插值的导数来逼近因变量的空间导数,再用修正的欧拉法逼近因变量的时间导数,得到数值算法。最后用该方法分别求得登革热模型的基本再生数大于1和小于1时的数值模拟图和数值解。Mathematical model is an important way to understand and control the spread of infectious diseases.In this paper,cubic B-spline quasi-interpolation method is used to solve a kind of dengue fever model with vertical transmission and time period.Firstly,the basic theory of cubic B-spline quasi-interpolation is introduced.Secondly,the derivative of the quasiinterpolation is applied to approximate the spatial derivative of the dependent variable,and the modified Euler method is used to approximate the time derivative of the dependent variable to obtain a numerical scheme.Finally,the numerical simulation diagrams and the numerical solutions are obtained when the basic regeneration number of the dengue fever model is greater than 1 and less than 1.

关 键 词：登革热数学模型 基本再生数 B样条拟插值 修正欧拉法 微分方程数值解 

分 类 号：O241.82[理学—计算数学]