Abstract
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.
Funding Statement
This work was supported by National Natural Science Foundation
of China [grant numbers 12001241 & 11731014], China Postdoctoral Science Foundation
[grant number 2018M642173], Basic Research Program of Jiangsu Province [grant number BK20200885]
and Jiangsu Key Lab for Numerical Simulation of Large Scale Complex Systems
[grant number 202006].
Acknowledgments
The authors are very grateful to the anonymous referee for his/her constructive comments and suggestions, which have helped to improve our original manuscript greatly.
Citation
Jingdong Wei. Zaili Zhen. Jiangbo Zhou. Lixin Tian. "Traveling Waves for a Discrete Diffusion Epidemic Model with Delay." Taiwanese J. Math. 25 (4) 831 - 866, August, 2021. https://doi.org/10.11650/tjm/201209
Information
