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Uniqueness of epidemic waves in a host-vector disease model


Authors: Zhaoquan Xu and Dongmei Xiao
Journal: Proc. Amer. Math. Soc. 146 (2018), 3875-3886
MSC (2010): Primary 35K57, 35R10, 92D30, 34K99
DOI: https://doi.org/10.1090/proc/14043
Published electronically: May 15, 2018
MathSciNet review: 3825841
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Abstract: A diffusive integro-differential equation which serves as a model for the evolution of a host-vector epidemic was extensively studied in literature. The traveling wave solutions of this model describe the spread of the disease from a disease-free state to an infective state, which are epidemic waves. It is a challenging problem if epidemic waves with the minimal propagation speed are unique up to translation. In this paper, we establish the uniqueness of all epidemic waves with any an admissible wave speed by the sliding method and solve this challenging problem completely.


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Additional Information

Zhaoquan Xu
Affiliation: Department of Mathematics, Jinan University, Guangzhou 510632, People’s Republic of China

Dongmei Xiao
Affiliation: School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
Email: xiaodm@sjtu.edu.cn

DOI: https://doi.org/10.1090/proc/14043
Keywords: Diffusive integro-differential equation, traveling wave solutions, uniqueness
Received by editor(s): June 26, 2017
Received by editor(s) in revised form: November 16, 2017
Published electronically: May 15, 2018
Additional Notes: The first author’s research was partially supported by the NNSF of China (No. 11701216), the NSF of Guangdong Province (No. 2017A030313015), and the Fundamental Research Funds for the Central Universities.
The second author is the corresponding author.
The second author’s research was partially supported by NNSF of China (No. 11431008 & No. 11371248).
Communicated by: Wenxian Shen
Article copyright: © Copyright 2018 American Mathematical Society