Traveling wave solutions for nonlocal dispersal Fisher–KPP model with age structure

2021 ◽  
pp. 107593
Author(s):  
Xuan Tian ◽  
Shangjiang Guo
Keyword(s):  
Age Structure ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Nonlocal 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.

Traveling wave solutions of a nonlocal dispersal SIRS model with spatio-temporal delay

2017 ◽  
Vol 10 (05) ◽  
pp. 1750071 ◽  
Author(s):  
Zhaohai Ma ◽  
Rong Yuan
Keyword(s):  
Fixed Point ◽  
Traveling Wave ◽  
Wave Speed ◽  
Traveling Wave Solutions ◽  
Temporal Delay ◽  
Nonlocal Dispersal ◽  
Wave Solutions ◽  
Sirs Model ◽  
Existence And Nonexistence ◽  
Spatio Temporal

This paper is mainly concerned with the existence and nonexistence of traveling wave solutions of a nonlocal dispersal SIRS model with nonlocal delayed transmissions. We find that the existence and nonexistence of traveling wave solutions are determined by the critical wave speed [Formula: see text]. More specifically, we establish the existence of traveling wave solutions for every wave speed [Formula: see text] and [Formula: see text] by means of upper-lower solutions and Schauder’s fixed point theorem. Nonexistence of traveling wave solutions is obtained by Laplace transform for any wave speed [Formula: see text] and [Formula: see text].

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