Uniqueness of epidemic waves in a host-vector disease model
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- by Zhaoquan Xu and Dongmei Xiao PDF
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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.References
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Additional Information
- Zhaoquan Xu
- Affiliation: Department of Mathematics, Jinan University, Guangzhou 510632, People’s Republic of China
- MR Author ID: 914388
- Dongmei Xiao
- Affiliation: School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
- MR Author ID: 256353
- Email: xiaodm@sjtu.edu.cn
- 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
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 3875-3886
- MSC (2010): Primary 35K57, 35R10, 92D30, 34K99
- DOI: https://doi.org/10.1090/proc/14043
- MathSciNet review: 3825841