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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2023, Vol. 40 ›› Issue (2): 281-294.doi: 10.3969/j.issn.1005-3085.2023.02.008

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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

钱  江,   陈雨青   

  1. 河海大学理学院，南京 211100
  • 收稿日期:2021-12-09 接受日期:2022-12-25 出版日期:2023-04-15 发布日期:2023-06-20
  • 基金资助:
    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).

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

QIAN Jiang,  CHEN Yuqing   

  1. College of Science, Hohai University, Nanjing 211100
  • Received:2021-12-09 Accepted:2022-12-25 Online:2023-04-15 Published:2023-06-20
  • Supported by:
    The National Natural Science Foundation of China (11601151); the Key Laboratory of Ministry of Education for Coastal Disaster and Protection, Hohai University (202011); the Natural Science Foundation of Jiangsu Province (BK20160853); the Fundamental Research Funds for the Central Universities of Hohai University (2016B08714; 2019B19414).

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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。

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

Abstract:

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 quasi-interpolation 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.

Key words: dengue fever mathematical model, basic reproduction number, B-spline quasi-interpolation, modified Euler method, numerical solution of differential equation

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