Traveling Waves for a Discrete Diffusion Epidemic Model with Delay

This paper is concerned with traveling wave solutions in a discrete diffusion epidemic model with delayed transmission. Employing the way of contradictory discussions and the bilateral Laplace transform, we obtain the nonexistence of nontrivial positive bounded traveling wave solutions. Utilizing th...

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Bibliographic Details
Published in:Taiwanese journal of mathematics 2021-08, Vol.25 (4), p.831-866
Main Authors: Wei, Jingdong, Zhen, Zaili, Zhou, Jiangbo, Tian, Lixin
Format: Article
Language:English
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Summary:This paper is concerned with traveling wave solutions in a discrete diffusion epidemic model with delayed transmission. Employing the way of contradictory discussions and the bilateral Laplace transform, we obtain the nonexistence of nontrivial positive bounded traveling wave solutions. Utilizing the super-/sub-solutions method and the fixed point theory, we derive the existence of nontrivial positive traveling wave solutions with both super-critical and critical speeds. Our results indicate that the critical speed is the minimal speed.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm/201209