scholarly journals The periodic traveling waves in a diffusive periodic SIR epidemic model with nonlinear incidence

2021 ◽  
Vol 144 ◽  
pp. 110683
Author(s):  
Weixin Wu ◽  
Zhidong Teng
Keyword(s):  
Traveling Waves ◽  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Nonlinear Incidence ◽  
Periodic Traveling Waves ◽  
Sir Epidemic

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.

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