Multi-dimensional discrete Halanay inequalities and the global stability of the disease free equilibrium of a discrete delayed malaria model

Advances in Difference Equations

Patricia JY Wong¹  Chunqing Wu² 

[1] School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore;School of Mathematics and Physics, Changzhou University, Changzhou, China

关键词: discrete Halanay-type inequalities;    multi-dimension;    global asymptotical stability;    nonsingular M-matrix;    malaria transmission;    time delay;   

DOI  :  10.1186/s13662-016-0840-4

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we establish two multi-dimensional discrete Halanay-type inequalities. As an application, we consider a malaria transmission model with two delays and employ the two discrete Halanay-type inequalities to establish the global (exponential) asymptotical stability of the disease free equilibrium of the model. It is further shown that the disease free equilibrium of the delayed model is globally asymptotically stable when the basic reproduction number of the model is less than 1.

【 授权许可】

CC BY