Can pathogen spread keep pace with its host invasion?

Jian Fang, Yijun Lou, Jianhong Wu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

62 Citations (Scopus)


We consider the Fisher-KPP equation in a wavelike shifting environment for which the wave profile of the environment is given by a monotonically decreasing function changing signs (shifting from favorable to unfavorable environment). This type of equation arises naturally from the consideration of pathogen spread in a classical susceptible-infected-susceptible epidemiological model of a host population where the disease impact on host mobility and mortality is negligible. We conclude that there are three different ranges of the disease transmission rate where the disease spread has distinguished spatiotemporal patterns: extinction; spread in pace with the host invasion; spread not in a wave format and slower than the host invasion. We calculate the disease propagation speed when disease does spread. Our analysis for a related elliptic operator provides closed form expressions for two generalized eigenvalues in an unbounded domain. The obtained closed forms yield unsolvability of the related elliptic equation in the critical case, which relates to the open problem 4.6 in.
Original languageEnglish
Pages (from-to)1633-1657
Number of pages25
JournalSIAM Journal on Applied Mathematics
Issue number4
Publication statusPublished - 1 Jan 2016


  • Disease spread
  • Fisher-KPP wave
  • Generalized eigenvalues
  • Pulse wave
  • Wavelike environment

ASJC Scopus subject areas

  • Applied Mathematics


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