scholarly journals Travelling Waves of a Diffusive Epidemic Model with Latency and Relapse

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Zhiping Wang ◽  
Rui Xu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Epidemic Model ◽  
Wave Solution ◽  
Local Stability ◽  
Travelling Waves ◽  
Upper And Lower Solutions ◽  
Travelling Wave ◽  
Spatial Diffusion ◽  
Travelling Wave Solution

An SEIR epidemic model with relapse and spatial diffusion is studied. By analyzing the corresponding characteristic equations, the local stability of each of the feasible steady states to this model is discussed. The existence of a travelling wave solution is established by using the technique of upper and lower solutions and Schauder's fixed point theorem. Numerical simulations are carried out to illustrate the main results.

TRAVELING WAVES OF AN EPIDEMIC MODEL WITH VACCINATION

2013 ◽  
Vol 06 (05) ◽  
pp. 1350033 ◽  
Author(s):  
ZHIPING WANG ◽  
RUI XU
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Epidemic Model ◽  
Wave Solution ◽  
Local Stability ◽  
Upper And Lower Solutions ◽  
Traveling Wave Solution ◽  
Spatial Diffusion

An epidemic model with vaccination and spatial diffusion is studied. By analyzing the corresponding characteristic equations, the local stability of each of feasible steady states to this model is discussed. The existence of a traveling wave solution is established by using the technique of upper and lower solutions and Schauder's fixed point theorem. Numerical simulations are carried out to illustrate the main results.

scholarly journals Travelling Waves of an n-Species Food Chain Model with Spatial Diffusion and Time Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Fei Hu ◽  
Yuyin Xu ◽  
Z. Wang ◽  
Wei Ding
Keyword(s):  
Fixed Point ◽  
Food Chain ◽  
Time Delays ◽  
Travelling Waves ◽  
Travelling Wave ◽  
Spatial Diffusion ◽  
Chain Model ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Food Chain Model

We investigate an n-species food chain model with spatial diffusion and time delays. By using Schauder’s fixed point theorem, we obtain the result about the existence of the travelling wave solutions of the food chain model with reaction term satisfying the partial quasimonotonicity conditions.

scholarly journals EVOLUTION OF MODULATIONAL INSTABILITY IN TRAVELLING WAVE SOLUTION OF NON-LINEAR PARTIAL DIFFERENTIAL EQUATION

2020 ◽  
Vol 5 (1) ◽  
pp. 1-7
Author(s):  
Ram Dayal Pankaj ◽  
Arun Kumar ◽  
Chandrawati Sindhi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Wave Solution ◽  
Modulational Instability ◽  
Nonlinear Partial Differential Equation ◽  
Linear Partial Differential Equation ◽  
Travelling Wave ◽  
Travelling Wave Solution ◽  
Partial Differential ◽  
Jacobian Elliptic Functions

The Ritz variational method has been applied to the nonlinear partial differential equation to construct a model for travelling wave solution. The spatially periodic trial function was chosen in the form of combination of Jacobian Elliptic functions, with the dependence of its parameters

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