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

In this paper, we develop the theory of basic reproduction ratios R 0 for abstract functional differential systems in a time-periodic environment. It is proved that R 0 - 1 has the same sign as the exponential growth bound of an associated linear system. Then we apply it to a time-periodic Lyme dise...

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Bibliographic Details
Published in:Journal of dynamics and differential equations 2019-09, Vol.31 (3), p.1247-1278
Main Authors: Liang, Xing, Zhang, Lei, Zhao, Xiao-Qiang
Format: Article
Language:English
Subjects:
Applications of Mathematics
Differential equations
Lyme disease
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
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Summary:In this paper, we develop the theory of basic reproduction ratios R 0 for abstract functional differential systems in a time-periodic environment. It is proved that R 0 - 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 .
ISSN:1040-7294
1572-9222
DOI:10.1007/s10884-017-9601-7