A PDE-ODE coupled spatio-temporal mathematical model for fire blight during bloom

Pupulin M., Wang X., Efendiev M. A., Giletti T., Eberl H. J.

Journal of Mathematical Biology, vol.91, no.6, 2025 (SCI-Expanded, Scopus) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 91 Issue: 6
  • Publication Date: 2025
  • Doi Number: 10.1007/s00285-025-02267-0
  • Journal Name: Journal of Mathematical Biology
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aquatic Science & Fisheries Abstracts (ASFA), BIOSIS, CAB Abstracts, MathSciNet, Veterinary Science Database, zbMATH
  • Keywords: Erwinia amylovora, Fire blight, Mathematical Model, PDE-ODE coupled system, Travelling Waves
  • Marmara University Affiliated: No

Abstract

Fire blight is a bacterial plant disease that affects apple and pear trees. We present a mathematical model for its spread in an orchard during bloom. This is a PDE-ODE coupled system, consisting of two semilinear PDEs for the pathogen, coupled to a system of three ODEs for the stationary hosts. Exploratory numerical simulations suggest the existence of travelling waves, which we subsequently prove, under some conditions on parameters, using the method of upper and lower bounds and Schauder’s fixed point theorem. Our results are likely not optimal in the sense that our constraints on parameters, which can be interpreted biologically, are sufficient for the existence of travelling waves, but probably not necessary. Possible implications for fire blight biology and management are discussed.