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

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.

scholarly journals Traveling waves in a nonlocal dispersal Kermack-McKendrick epidemic model

2013 ◽  
Vol 18 (7) ◽  
pp. 1969-1993 ◽  
Author(s):  
Fei-Ying Yang ◽  
◽  
Yan Li ◽  
Wan-Tong Li ◽  
Zhi-Cheng Wang ◽  
...  
Keyword(s):  
Traveling Waves ◽  
Epidemic Model ◽  
Nonlocal Dispersal

scholarly journals Traveling waves in nonlocal dispersal SIR epidemic model with nonlinear incidence and distributed latent delay

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Weixin Wu ◽  
Zhidong Teng
Keyword(s):  
Traveling Waves ◽  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Nonlocal Dispersal ◽  
Solution Map ◽  
Nonlinear Incidence ◽  
Nonexistence Result ◽  
Sir Epidemic ◽  
Minimal Wave Speed ◽  
The Fixed Point Theorem

Abstract This paper studies the traveling waves in a nonlocal dispersal SIR epidemic model with nonlinear incidence and distributed latent delay. It is found that the traveling waves connecting the disease-free equilibrium with endemic equilibrium are determined by the basic reproduction number $\mathcal{R}_{0}$ R 0 and the minimal wave speed $c^{*}$ c ∗ . When $\mathcal{R}_{0}>1$ R 0 > 1 and $c>c^{*}$ c > c ∗ , the existence of traveling waves is established by using the upper-lower solutions, auxiliary system, constructing the solution map, and then the fixed point theorem, limiting argument, diagonal extraction method, and Lyapunov functions. When $\mathcal{R}_{0}>1$ R 0 > 1 and $0< c< c^{*}$ 0 < c < c ∗ , the nonexistence result is also obtained by using the reduction to absurdity and the theory of asymptotic spreading.

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>

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
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