Basic reproduction ratios for periodic and time-delayed compartmental models with impulses

被引：16
作者：
Bai, Zhenguo [1 ]
Zhao, Xiao-Qiang [2 ]
机构：
[1] Xidian Univ, Sch Math & Stat, Xian 710071, Peoples R China
[2] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada
来源：
JOURNAL OF MATHEMATICAL BIOLOGY | 2020年 / 80卷 / 04期
关键词：
Impulsive models; Time delay; Basic reproduction ratio; Computer virus; Threshold dynamics; VECTOR-BORNE DISEASES; STRUCTURED POPULATION; THRESHOLD DYNAMICS; EPIDEMIC MODELS; SPREAD; NUMBER;
D O I：
10.1007/s00285-019-01452-2
中图分类号：
Q [生物科学];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
Much work has focused on the basic reproduction ratio R0 for a variety of compartmental population models, but the theory of R0remains unsolved for periodic and time-delayed impulsive models. In this paper, we develop the theory of R0 for a class of such impulsive models. We first introduce R0and show that it is a threshold parameter for the stability of the zero solution of an associated linear system. Then we apply this theory to a time-delayed computer virus model with impulse treatment and obtain a threshold result on its global dynamics in terms of R0 Numerically, it is found that the basic reproduction ratio of the time-averaged delayed impulsive system may overestimate the spread risk of the virus.
引用
收藏
页码：1095 / 1117
页数：23
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