Existence of entire solutions for delayed monostable epidemic models

Shi Liang Wu, Cheng Hsiung Hsu

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


The purpose of this work is to study the existence of entire solutions for delayed monostable epidemic models with and without the quasi-monotone condition. In the quasi-monotone case, we first establish the comparison principle and construct appropriate sub-solutions and upper estimates. Then the existence and qualitative features of entire solutions are proved by mixing any finite number of traveling wave fronts with different speeds c ≥cmin and directions and a spatially independent solution, where cmin > 0 is the critical wave speed. In the non-quasi-monotone case, some new types of entire solutions are constructed by using the traveling wave fronts and spatially independent solutions of two auxiliary quasi-monotone systems and a comparison theorem for the Cauchy problems of the three systems.

Original languageEnglish
Pages (from-to)6033-6062
Number of pages30
JournalTransactions of the American Mathematical Society
Issue number9
StatePublished - 2016


  • Delayed reaction-diffusion system
  • Entire solution
  • Spatially independent heteroclinic orbit
  • Traveling wave front


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