Positive explicit and implicit computational techniques for reaction–diffusion epidemic model of dengue disease dynamics

Advances in Difference Equations

article

Ahmed, Nauman¹  Rafiq, Muhammad³  Baleanu, Dumitru⁴  Alshomrani, Ali Saleh⁷  Rehman, Muhammad Aziz-ur¹ 

[1] Department of Mathematics, University of Management and Technology;Department of Mathematics and Statistics, The University of Lahore;Faculty of Engineering, University of Central Punjab;Department of Mathematics, Cankaya University;Department of Medical Research, China Medical University Hospital, China Medical University;Institute of Space Sciences;Faculty of Science, Department of Mathematics, King Abdulaziz University

关键词: Structure preserving methods;    Finite difference schemes;    Dengue model;    Diffusion epidemic system;    Numerical simulations;   

DOI  :  10.1186/s13662-020-02622-z

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

The aim of this work is to develop a novel explicit unconditionally positivity preserving finite difference (FD) scheme and an implicit positive FD scheme for the numerical solution of dengue epidemic reaction–diffusion model with incubation period of virus. The proposed schemes are unconditionally stable and preserve all the essential properties of the solution of the dengue reaction diffusion model. This proposed FD schemes are unconditionally dynamically consistent with positivity property and converge to the true equilibrium points of dengue epidemic reaction diffusion system. Comparison of the proposed scheme with the well-known existing techniques is also presented. The time efficiency of both the proposed schemes is also compared, with the two widely used techniques.

【 授权许可】

CC BY