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

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 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 with critical speed in a delayed diffusive epidemic model

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yueling Cheng ◽  
Dianchen Lu ◽  
Jiangbo Zhou ◽  
Jingdong Wei
Keyword(s):  
Traveling Wave ◽  
Epidemic Model ◽  
Traveling Wave Solutions ◽  
Traveling Wave Solution ◽  
Sir Epidemic Model ◽  
Open Problems ◽  
Sir Epidemic ◽  
Nonlinear Anal ◽  
Wave Solutions ◽  
Saturated Incidence

AbstractIn this paper, we prove the existence of a critical traveling wave solution for a delayed diffusive SIR epidemic model with saturated incidence. Moreover, we establish the nonexistence of traveling wave solutions with nonpositive wave speed for this model. Our results solve some open problems left in the recent paper (Z. Xu in Nonlinear Anal. 111:66–81, 2014).

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