Abstract
In view of the infected individuals with the ability to move freely and spread disease, the traveling wave solutions for nonlocal dispersal SIR models with spatiotemporal delays were investigated. The threshold dynamics was determined by means of the basic reproduction number and the minimal wave speed. Firstly, based on Schauder’s fixed point theorem, the existence of fixed points on the cone was proved through construction of an invariant cone of the initial function on a bounded region. Then, the nonexistence of traveling wave solutions was verified through the twosided Laplace transform. Since the minimum propagation velocity of the traveling wave solution had important practical significance to control the disease transmission, the influences of the nonlocal diffusion term and the delay on the minimum wave velocity of the disease were discussed.
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