Critical periodic traveling waves for a periodic and diffusive epidemic model

ABSTRACT

This work is devoted to the existence of time periodic traveling wave solutions with critical speed $c^{\ast }$ for a seasonal and diffusive epidemic model. We adopt the approach of super- and sub-solutions and Schauder's fixed point theorem to the truncated problem combined with limiting arguments to obtain the existence of critical periodic traveling waves. This would be appropriate for the modification versions of current model, where standard incidence is replaced by other nonlinear incidence.

KEYWORDS:

• Periodic traveling wave solutions
• critical speed
• time periodic and diffusive
• epidemic model

AMS SUBJECT CLASSIFICATIONS (2000):

• 35K57
• 35B40
• 92D30

Acknowledgments

The authors are grateful to the anonymous referees for their insightful comments and suggestions which contributed to greatly improve the original version of the manuscript. The authors would like to thank Prof. Zhi-Cheng Wang for helpful discussions on this project.

Disclosure statement

No potential conflict of interest was reported by the authors.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

NNSF of China (11701242) the Fundamental Research Funds for the Central Universities (lzujbky2019-79). Science and Technology Planed Projects of Gansu Province (18JR3RA217).