Traveling wave solutions for a SEIR epidemic model in combination with random dispersal and nonlocal dispersal

2020 ◽  
Vol 32 (2) ◽  
pp. 213-237
Author(s):  
Xin Wu ◽  
Rong Yuan ◽  
Baochuan Tian
Keyword(s):  
Traveling Wave ◽  
Epidemic Model ◽  
Traveling Wave Solutions ◽  
Nonlocal Dispersal ◽  
Random Dispersal ◽  
Wave Solutions

scholarly journals Traveling Waves in a Nonlocal Dispersal SIR Model with Standard Incidence Rate and Nonlocal Delayed Transmission

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 641 ◽  
Author(s):  
Kuilin Wu ◽  
Kai Zhou
Keyword(s):  
Incidence Rate ◽  
Traveling Wave ◽  
Epidemic Model ◽  
Reaction System ◽  
Traveling Wave Solutions ◽  
Sir Epidemic Model ◽  
Nonlocal Dispersal ◽  
Sir Epidemic ◽  
Wave Solutions ◽  
Minimal Wave Speed

In this paper, we study the traveling wave solutions for a nonlocal dispersal SIR epidemic model with standard incidence rate and nonlocal delayed transmission. The existence and nonexistence of traveling wave solutions are determined by the basic reproduction number of the corresponding reaction system and the minimal wave speed. To prove these results, we apply the Schauder’s fixed point theorem and two-sided Laplace transform. The main difficulties are that the complexity of the incidence rate in the epidemic model and the lack of regularity for nonlocal dispersal operator.

scholarly journals Existence of traveling wave solutions for a delayed nonlocal dispersal SIR epidemic model with the critical wave speed

2021 ◽  
Vol 18 (6) ◽  
pp. 9357-9380
Author(s):  
Shiqiang Feng ◽  
◽  
Dapeng Gao ◽  
Keyword(s):  
Traveling Waves ◽  
Traveling Wave ◽  
Epidemic Model ◽  
Wave Speed ◽  
Traveling Wave Solutions ◽  
Auxiliary System ◽  
Sir Epidemic Model ◽  
Nonlocal Dispersal ◽  
Sir Epidemic ◽  
Wave Solutions

<abstract><p>This paper is about the existence of traveling wave solutions for a delayed nonlocal dispersal SIR epidemic model with the critical wave speed. Because of the introduction of nonlocal dispersal and the generality of incidence function, it is difficult to investigate the existence of critical traveling waves. To this end, we construct an auxiliary system and show the existence of traveling waves for the auxiliary system. Employing the results for the auxiliary system, we obtain the existence of traveling waves for the delayed nonlocal dispersal SIR epidemic model with the critical wave speed under mild conditions.</p></abstract>

Minimal wave speed of a diffusive SIR epidemic model with nonlocal delay

2019 ◽  
Vol 12 (07) ◽  
pp. 1950081
Author(s):  
Fuzhen Wu ◽  
Dongfeng Li
Keyword(s):  
Traveling Wave ◽  
Epidemic Model ◽  
Wave Speed ◽  
Traveling Wave Solutions ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Nonlocal Delay ◽  
Spatial Nonlocality ◽  
Wave Solutions ◽  
Minimal Wave Speed

This paper is concerned with the minimal wave speed in a diffusive epidemic model with nonlocal delays. We define a threshold. By presenting the existence and the nonexistence of traveling wave solutions for all positive wave speed, we confirm that the threshold is the minimal wave speed of traveling wave solutions, which models that the infective invades the habitat of the susceptible. For some cases, it is proven that spatial nonlocality may increase the propagation threshold while time delay decreases the threshold.

scholarly journals Traveling wave solutions for a diffusive sis epidemic model

2013 ◽  
Vol 18 (5) ◽  
pp. 1291-1304 ◽  
Author(s):  
Wei Ding ◽  
◽  
Wenzhang Huang ◽  
Siroj Kansakar ◽  
Keyword(s):  
Traveling Wave ◽  
Epidemic Model ◽  
Traveling Wave Solutions ◽  
Sis Epidemic Model ◽  
Wave Solutions ◽  
Sis Epidemic
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