Journal of Dynamical and Control Systems

, Volume 25, Issue 2, pp 175–195 | Cite as

Stability of Traveling Wavefronts for a Nonlocal Dispersal System with Delay

  • Zhihua Guo
  • Shi-Liang WuEmail author


This paper is concerned with a nonlocal epidemic model arising from the spread of an epidemic by oral-fecal transmission. Comparing with the previous works, here we extend the model in Capasso and Maddalena, Nonlinear Phenom Math Sci. 41:207–217 (1982) by including a spatial convolution term and a discrete delay term corresponding to the dispersal of bacteria in the environment and the latent period of the virus, respectively. Besides existence and asymptotic behavior, the main part of the paper is devoted to the stability of the traveling wavefronts under some monostable assumptions. By using a comparison theorem and the weighted energy method with a suitably selected weight function, we show that all the non-critical traveling waves are exponentially stable. Finally, we apply our results to a specific epidemic model and discuss the effect of time delay on the stability of wavefront.


Traveling wavefront Nonlocal dispersal system Stability Weighted energy method 

Mathematics Subject Classification (2010)

35K57 92D25 92D30 



We are very grateful to the referees for their helpful comments and suggestions which led to an improvement of our original manuscript.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXidian University Xi’anShaanxiPeople’s Republic of China

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