scholarly journals Traveling waves in a nonlocal dispersal epidemic model with spatio-temporal delay

2020 ◽  
Vol 19 (5) ◽  
pp. 2853-2886
Author(s):  
Jingdong Wei ◽  
◽  
Jiangbo Zhou ◽  
Wenxia Chen ◽  
Zaili Zhen ◽  
...  
Keyword(s):  
Traveling Waves ◽  
Epidemic Model ◽  
Temporal Delay ◽  
Nonlocal Dispersal ◽  
Spatio Temporal

scholarly journals Traveling waves for SVIR epidemic model with nonlocal dispersal

2019 ◽  
Vol 16 (3) ◽  
pp. 1654-1682
Author(s):  
Ran Zhang ◽  
◽  
Shengqiang Liu
Keyword(s):  
Traveling Waves ◽  
Epidemic Model ◽  
Nonlocal Dispersal

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].

scholarly journals Traveling waves for a nonlocal dispersal SIR epidemic model with the mass action infection mechanism

2021 ◽  
Author(s):  
Xin Wu ◽  
Zhaohai Ma
Keyword(s):  
Equilibrium State ◽  
Traveling Waves ◽  
Epidemic Model ◽  
Mass Action ◽  
Sir Epidemic Model ◽  
Nonlocal Dispersal ◽  
New Model ◽  
Infection Mechanism ◽  
Sir Epidemic ◽  
Lasalle Theorem

This paper is concerned with a nonlocal dispersal susceptible–infected–recovered (SIR) epidemic model adopted with the mass action infection mechanism. We mainly study the existence and non-existence of traveling waves connecting the infection-free equilibrium state and the endemic equilibrium state. The main difficulties lie in the fact that the semiflow generated here does not admit the order-preserving property. Meanwhile, this new model brings some new challenges due to the unboundedness of the nonlinear term. We overcome these difficulties to obtain the boundedness of traveling waves with the speed $c>c_{\min}$ by some analysis techniques firstly and then prove the existence of traveling waves by employing Lyapunov–LaSalle theorem and Lebesgue dominated convergence theorem. By utilizing a approximating method, we study the existence of traveling waves with the critical wave speed $c_{\min}$. Our results on this new model may provide some implications on disease modelling and controls.

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