The formation of spreading front: the singular limit of three-component reaction–diffusion models

Hirofumi Izuhara, Harunori Monobe, Chang Hong Wu

    Research output: Contribution to journalArticlepeer-review

    Abstract

    Understanding the invasion processes of biological species is a fundamental issue in ecology. Several mathematical models have been proposed to estimate the spreading speed of species. In recent decades, it was reported that some mathematical models of population dynamics have an explicit form of the evolution equations for the spreading front, which are represented by free boundary problems such as the Stefan-like problem (e.g., Mimura et al., Jpn J Appl Math 2:151–186, 1985; Du and Lin, SIAM J Math Anal 42:377–405, 2010). To understand the formation of the spreading front, in this paper, we will consider the singular limit of three-component reaction–diffusion models and give some interpretations for spreading front from the viewpoint of modeling. As an application, we revisit the issue of the spread of the grey squirrel in the UK and estimate the spreading speed of the grey squirrel based on our result. Also, we discuss the relation between some free boundary problems related to population dynamics and mathematical models describing Controlling Invasive Alien Species. Lastly, we numerically consider the traveling wave solutions, which give information on the spreading behavior of invasive species.

    Original languageEnglish
    Article number38
    JournalJournal of Mathematical Biology
    Volume82
    Issue number5
    DOIs
    Publication statusPublished - Apr 2021

    Keywords

    • Free boundary problems
    • Reaction–diffusion systems
    • Singular limit
    • Spreading front
    • Traveling waves

    ASJC Scopus subject areas

    • Modelling and Simulation
    • Agricultural and Biological Sciences (miscellaneous)
    • Applied Mathematics

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