Wave propagation in a infectious disease model with non-local diffusion

Autor: Yueling Cheng, Dianchen Lu
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Zdroj: Advances in Difference Equations, Vol 2019, Iss 1, Pp 1-29 (2019)
Druh dokumentu: article
ISSN: 1687-1847
03640795
DOI: 10.1186/s13662-019-2057-9
Popis: Abstract In this paper, we propose a nonlocal diffusion infectious disease model with nonlinear incidences and distributed delay to model the transmission of the epidemic. By a fixed point theorem and a limiting argument, we establish the existence of traveling wave solutions for the model. Meanwhile, we obtain the non-existence of traveling wave solutions for the model via two-sided Laplace transform. It is found that the threshold dynamics of traveling wave solutions are entirely determined by the basic reproduction number of the corresponding spatially-homogenous delayed differential system and the minimum wave speed. A typical example is given for supporting our abstract results. Moreover, the effect of the diffusive rate of the infected individuals on the minimum wave speed is discussed.
Databáze: Directory of Open Access Journals
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