Basic Reproduction Ratios for Periodic Abstract Functional Differential Equations (with Application to a Spatial Model for Lyme Disease)

被引：149
作者：
Liang, Xing [1 ]
Zhang, Lei [1 ,2 ]
Zhao, Xiao-Qiang [2 ]
机构：
[1] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China
[2] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada
来源：
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2019年 / 31卷 / 03期
基金：
中国国家自然科学基金; 加拿大自然科学与工程研究理事会;
关键词：
Basic reproduction ratio; Abstract functional differential system; Periodic solution; Lyme disease; Threshold dynamics; THRESHOLD DYNAMICS; EPIDEMIC; SYSTEMS; SEASONALITY; PERSISTENCE; STABILITY; NUMBERS; R-0;
D O I：
10.1007/s10884-017-9601-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we develop the theory of basic reproduction ratios R0 for abstract functional differential systems in a time-periodic environment. It is proved that R0 - 1 has the same sign as the exponential growth bound of an associated linear system. Then we apply it to a time-periodic Lyme disease model with time-delay and obtain a threshold type result on its global dynamics in terms of R-0.
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页码：1247 / 1278
页数：32
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