Wave propagation in a nonlocal dispersal SIR epidemic model with nonlinear incidence and nonlocal distributed delays

2020 ◽  
Vol 61 (6) ◽  
pp. 061512
Author(s):  
Weixin Wu ◽  
Long Zhang ◽  
Zhidong Teng
Keyword(s):  
Wave Propagation ◽  
Epidemic Model ◽  
Distributed Delays ◽  
Sir Epidemic Model ◽  
Nonlocal Dispersal ◽  
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 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.

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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