Spatial dynamics of a nonlocal model with periodic delay and competition

L. Zhang, K. H. Liu, Y. J. Lou, Z. C. Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)


Each species is subject to various biotic and abiotic factors during growth. This paper formulates a deterministic model with the consideration of various factors regulating population growth such as age-dependent birth and death rates, spatial movements, seasonal variations, intra-specific competition and time-varying maturation simultaneously. The model takes the form of two coupled reaction-diffusion equations with time-dependent delays, which bring novel challenges to the theoretical analysis. Then, the model is analysed when competition among immatures is neglected, in which situation one equation for the adult population density is decoupled. The basic reproduction number R0 is defined and shown to determine the global attractivity of either the zero equilibrium (when R0 ≤ 1) or a positive periodic solution (R0> 1) by using the dynamical system approach on an appropriate phase space. When the immature intra-specific competition is included and the immature diffusion rate is neglected, the model is neither cooperative nor reducible to a single equation. In this case, the threshold dynamics about the population extinction and uniform persistence are established by using the newly defined basic reproduction number R0 as a threshold index. Furthermore, numerical simulations are implemented on the population growth of two different species for two different cases to validate the analytic results.

Original languageEnglish
Pages (from-to)1070-1100
Number of pages31
JournalEuropean Journal of Applied Mathematics
Early online date6 Jan 2020
Publication statusE-pub ahead of print - 6 Jan 2020


  • Age structure
  • Diffusion
  • Intra-specific competition
  • Periodic delay
  • Seasonal effects

ASJC Scopus subject areas

  • Applied Mathematics


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