Traveling waves in a nonlocal dispersal Kermack-McKendrick epidemic model

By Fei-Ying Yang, Yan Li, Wan-Tong Li, Zhi-Cheng Wang. 2013

94 citations recorded by the source corpus.

In this paper, we consider a Kermack-McKendrick epidemic model with nonlocal dispersal. We find that the existence and nonexistence of traveling wave solutions are determined by the reproduction number. To prove the existence of nontrivial traveling wave solutions, we construct an invariant cone in a bounded domain with initial functions being defined on, and apply Schauder's fixed point theorem as well as limiting argument. Here, the compactness of the support set of dispersal kernel is needed when passing to an unbounded domain in the proof. Moreover, the nonexistence of traveling wave solutions is obtained by Laplace transform if the speed is less than the critical velocity.

Subfields: Applied Mathematics, Mathematical Physics, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/244ef15226b8039faf856f4df77744f088773d94

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In Applied Mathematics

In Mathematical Physics

In Public Health, Environmental and Occupational Health

Citations in the corpus

Propagation phenomena for a two-species Lotka–Volterra strong competition system with nonlocal dispersal (2019, background): “Nonlocal dispersal systems can be found in many applied subjects such as population biology, epidemiology, phase transition, signal propagation in neural networks and so on [2,12,24,34,41].”