Traveling waves in a delayed SIR epidemic model with nonlinear incidence

2015 ◽  
Vol 263 ◽  
pp. 221-232 ◽  
Author(s):  
Zhenguo Bai ◽  
Shi-Liang Wu
Keyword(s):  
Traveling Waves ◽  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Nonlinear Incidence ◽  
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.

scholarly journals Stability Analysis of a Stochastic SIR Epidemic Model with Specific Nonlinear Incidence Rate

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Jihad Adnani ◽  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Endemic Equilibrium ◽  
Random Perturbations ◽  
Sir Epidemic Model ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Sir Epidemic ◽  
Stochastic Sir ◽  
The Stability

We investigate a stochastic SIR epidemic model with specific nonlinear incidence rate. The stochastic model is derived from the deterministic epidemic model by introducing random perturbations around the endemic equilibrium state. The effect of random perturbations on the stability behavior of endemic equilibrium is discussed. Finally, numerical simulations are presented to illustrate our theoretical results.

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