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Wave propagation in a diffusive SEIR epidemic model with nonlocal reaction and standard incidence rate
Author(s) -
Wu Xin,
Tian Baochuan,
Yuan Rong
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5273
Subject(s) - mathematics , reaction–diffusion system , laplace transform , traveling wave , wave speed , mathematical analysis , epidemic model , ordinary differential equation , basic reproduction number , fixed point theorem , population , differential equation , demography , sociology
We study the existence and nonexistence of traveling waves of the reaction‐diffusion equations that describes a diffusive SEIR model with nonlocal reaction between the infected subpopulation and the susceptible subpopulation, where the total population is not constant. The existence of traveling waves depends on the basic reproduction number R 0 of the corresponding ordinary differential equations and the minimal wave speed c ∗ . The main difficulty is the lack of order‐preserving property of our general system. Its proof is showed by constructing a closed and convex set and applying Schauder fixed point theorem. The proof of nonexistence result is obtained by two‐side Laplace transform. Finally, we present some numerical results of the minimal wave speed.