Minimal wave speed in a diffusive epidemic model with temporal delay

2007 ◽  
Vol 188 (1) ◽  
pp. 275-280 ◽  
Author(s):  
Guosheng Zhang ◽  
Yifu Wang
Keyword(s):  
Epidemic Model ◽  
Wave Speed ◽  
Temporal Delay ◽  
Minimal Wave Speed

Minimal wave speed of a diffusive SIR epidemic model with nonlocal delay

2019 ◽  
Vol 12 (07) ◽  
pp. 1950081
Author(s):  
Fuzhen Wu ◽  
Dongfeng Li
Keyword(s):  
Traveling Wave ◽  
Epidemic Model ◽  
Wave Speed ◽  
Traveling Wave Solutions ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Nonlocal Delay ◽  
Spatial Nonlocality ◽  
Wave Solutions ◽  
Minimal Wave Speed

This paper is concerned with the minimal wave speed in a diffusive epidemic model with nonlocal delays. We define a threshold. By presenting the existence and the nonexistence of traveling wave solutions for all positive wave speed, we confirm that the threshold is the minimal wave speed of traveling wave solutions, which models that the infective invades the habitat of the susceptible. For some cases, it is proven that spatial nonlocality may increase the propagation threshold while time delay decreases the threshold.

TRAVELING WAVES FOR A SIMPLE DIFFUSIVE EPIDEMIC MODEL

1995 ◽  
Vol 05 (07) ◽  
pp. 935-966 ◽  
Author(s):  
YUZO HOSONO ◽  
BILAL ILYAS
Keyword(s):  
Traveling Wave ◽  
Epidemic Model ◽  
Wave Speed ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Shooting Argument ◽  
Wave Solutions ◽  
Minimal Wave Speed ◽  
Manifold Theory

We investigate the existence of traveling wave solutions for the infective-susceptible two-component epidemic model. The model system is described by reaction-diffusion equations with the nonlinear reaction term of the classical Kermack-McKendric type. The diffusion coefficients of infectives and susceptibles are assumed to be positive constants d1 and d2 respectively. By the shooting argument with the aid of the invariant manifold theory, we prove that there exists a positive constant c* such that the traveling wave solutions exist for any c≥c*. The minimal wave speed c* is shown to be independent of d2 and to have the same value as that for d2=0.

scholarly journals Traveling Wave Solutions in a Reaction-Diffusion Epidemic Model

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Sheng Wang ◽  
Wenbin Liu ◽  
Zhengguang Guo ◽  
Weiming Wang
Keyword(s):  
Traveling Wave ◽  
Epidemic Model ◽  
Wave Speed ◽  
Upper And Lower Solutions ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Monotone Iteration ◽  
Wave Solutions ◽  
Minimal Wave Speed

We investigate the traveling wave solutions in a reaction-diffusion epidemic model. The existence of the wave solutions is derived through monotone iteration of a pair of classical upper and lower solutions. The traveling wave solutions are shown to be unique and strictly monotonic. Furthermore, we determine the critical minimal wave speed.

scholarly journals Minimal Wave Speed in a Predator-Prey System with Distributed Time Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Fuzhen Wu ◽  
Dongfeng Li
Keyword(s):  
Time Delay ◽  
Traveling Wave ◽  
Wave Speed ◽  
Upper And Lower Solutions ◽  
Traveling Wave Solutions ◽  
Predator Prey ◽  
Wave Solutions ◽  
Prey System ◽  
Minimal Wave Speed ◽  
Distributed Time Delay

This paper is concerned with the minimal wave speed of traveling wave solutions in a predator-prey system with distributed time delay, which does not satisfy comparison principle due to delayed intraspecific terms. By constructing upper and lower solutions, we obtain the existence of traveling wave solutions when the wave speed is the minimal wave speed. Our results complete the known conclusions and show the precisely asymptotic behavior of traveling wave solutions.

Selection mechanism of the minimal wave speed to the Lotka–Volterra competition model

2020 ◽  
Vol 104 ◽  
pp. 106281
Author(s):  
Manjun Ma ◽  
Dong Chen ◽  
Jiajun Yue ◽  
Yazhou Han
Keyword(s):  
Wave Speed ◽  
Competition Model ◽  
Selection Mechanism ◽  
Minimal Wave Speed

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 Existence of Traveling Wave Solutions for Cholera Model

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Tianran Zhang ◽  
Qingming Gou ◽  
Xiaoli Wang
Keyword(s):  
Traveling Wave ◽  
Wave Speed ◽  
Shooting Method ◽  
Reproduction Number ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Traveling Wave Solution ◽  
Reaction Diffusion Model ◽  
Minimal Wave Speed ◽  
The Basic Reproduction Number

To investigate the spreading speed of cholera, Codeço’s cholera model (2001) is developed by a reaction-diffusion model that incorporates both indirect environment-to-human and direct human-to-human transmissions and the pathogen diffusion. The two transmission incidences are supposed to be saturated with infective density and pathogen density. The basic reproduction numberR0is defined and the formula for minimal wave speedc*is given. It is proved by shooting method that there exists a traveling wave solution with speedcfor cholera model if and only ifc≥c*.

scholarly journals The Minimal Wave Speed of a Lotka-Volterra Competition Model

2021 ◽  
Vol 42 (6) ◽  
pp. 575-585
Author(s):  
ZHANG Yafei ◽  
◽  
◽  
ZHOU Yinbo
Keyword(s):  
Wave Speed ◽  
Competition Model ◽  
Minimal Wave Speed
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