ZOU Xia. Traveling Wave Solutions for Nonlocal Dispersal SIR Models With Spatio-Temporal Delays[J]. Applied Mathematics and Mechanics, 2018, 39(5): 611-630. doi: 10.21656/1000-0887.380118
Citation: ZOU Xia. Traveling Wave Solutions for Nonlocal Dispersal SIR Models With Spatio-Temporal Delays[J]. Applied Mathematics and Mechanics, 2018, 39(5): 611-630. doi: 10.21656/1000-0887.380118

Traveling Wave Solutions for Nonlocal Dispersal SIR Models With Spatio-Temporal Delays

doi: 10.21656/1000-0887.380118
Funds:  The National Natural Science Foundation of China(11671315)
  • Received Date: 2017-05-02
  • Rev Recd Date: 2018-04-01
  • Publish Date: 2018-05-15
  • 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 spatiotemporal 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 nonexistence of traveling wave solutions was verified through the twosided 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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