scholarly journals Traveling Wave Solutions for a Delayed SIRS Infectious Disease Model with Nonlocal Diffusion and Nonlinear Incidence

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Xiaohong Tian ◽  
Rui Xu
Keyword(s):  
Infectious Disease ◽  
Steady State ◽  
Traveling Wave ◽  
Disease Model ◽  
Traveling Wave Solutions ◽  
Traveling Wave Solution ◽  
Nonlocal Diffusion ◽  
Nonlinear Incidence ◽  
Infectious Disease Model ◽  
Disease Free

A delayed SIRS infectious disease model with nonlocal diffusion and nonlinear incidence is investigated. By constructing a pair of upper-lower solutions and using Schauder's fixed point theorem, we derive the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady state.

scholarly journals Stability Analysis of an Age-Structured SEIRS Model with Time Delay

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 455 ◽  
Author(s):  
Zhe Yin ◽  
Yongguang Yu ◽  
Zhenzhen Lu
Keyword(s):  
Time Delay ◽  
Equilibrium Point ◽  
Traveling Wave ◽  
Wave Solution ◽  
Disease Model ◽  
Endemic Equilibrium ◽  
Traveling Wave Solution ◽  
Age Structured ◽  
Nonlinear Autonomous System ◽  
Disease Free

This paper is concerned with the stability of an age-structured susceptible–exposed– infective–recovered–susceptible (SEIRS) model with time delay. Firstly, the traveling wave solution of system can be obtained by using the method of characteristic. The existence and uniqueness of the continuous traveling wave solution is investigated under some hypotheses. Moreover, the age-structured SEIRS system is reduced to the nonlinear autonomous system of delay ODE using some insignificant simplifications. It is studied that the dimensionless indexes for the existence of one disease-free equilibrium point and one endemic equilibrium point of the model. Furthermore, the local stability for the disease-free equilibrium point and the endemic equilibrium point of the infection-induced disease model is established. Finally, some numerical simulations were carried out to illustrate our theoretical results.

TRAVELING WAVE SOLUTIONS IN A THREE-SPECIES FOOD-CHAIN MODEL WITH DIFFUSION AND DELAYS

2012 ◽  
Vol 05 (01) ◽  
pp. 1250002 ◽  
Author(s):  
YANKE DU ◽  
RUI XU
Keyword(s):  
Steady State ◽  
Food Chain ◽  
Traveling Wave ◽  
Time Delays ◽  
Traveling Wave Solutions ◽  
Iteration Scheme ◽  
Traveling Wave Solution ◽  
Chain Model ◽  
Wave Solutions ◽  
Food Chain Model

This paper deals with the existence of traveling wave solutions in a three-species food-chain model with spatial diffusion and time delays due to gestation and negative feedback. By using a cross iteration scheme and Schauder's fixed point theorem, we reduce the existence of traveling wave solutions to the existence of a pair of upper-lower solutions. By constructing a pair of upper-lower solutions, we derive the existence of a traveling wave solution connecting the trivial steady state and the positive steady state. Numerical simulations are carried out to illustrate the main results. In particular, our results extend and improve some known results.

scholarly journals Single peaked traveling wave solutions to a generalized μ-Novikov Equation

2020 ◽  
Vol 10 (1) ◽  
pp. 66-75
Author(s):  
Byungsoo Moon
Keyword(s):  
Linear Combination ◽  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solutions ◽  
Traveling Wave Solution ◽  
Wave Solutions ◽  
Quadratic Nonlinearities ◽  
Novikov Equation

Abstract In this paper, we study the existence of peaked traveling wave solution of the generalized μ-Novikov equation with nonlocal cubic and quadratic nonlinearities. The equation is a μ-version of a linear combination of the Novikov equation and Camassa-Hom equation. It is found that the equation admits single peaked traveling wave solutions.

STABILITY OF STEADY STATE AND TRAVELING WAVES SOLUTIONS IN COUPLED MAP LATTICES

2008 ◽  
Vol 18 (01) ◽  
pp. 219-225 ◽  
Author(s):  
DANIEL TURZÍK ◽  
MIROSLAVA DUBCOVÁ
Keyword(s):  
Steady State ◽  
Essential Spectrum ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Linear Operators ◽  
Coupled Map Lattices ◽  
Basic Tool ◽  
Wave Solutions ◽  
The Stability

We determine the essential spectrum of certain types of linear operators which arise in the study of the stability of steady state or traveling wave solutions in coupled map lattices. The basic tool is the Gelfand transformation which enables us to determine the essential spectrum completely.

scholarly journals Obesity as an "infectious" disease

2021 ◽  
Vol 11 (9) ◽  
pp. 534-537
Author(s):  
Daria Żuraw ◽  
Paulina Oleksa ◽  
Mateusz Sobczyk
Keyword(s):  
Infectious Disease ◽  
Disease Model ◽  
Living Environment ◽  
Social Contagion ◽  
Social Discrimination ◽  
Obese People ◽  
Obesity Epidemic ◽  
Global Epidemic ◽  
Infectious Disease Model ◽  
The One

Introduction: Obesity has been recognized as a global epidemic by the WHO, followed by a wealth of empirical evidence supporting its contagiousness. However, the dynamics of the spread of obesity between individuals are rarely studied.  A distinguishing feature of the obesity epidemic is that it is driven by a process of social contagion that cannot be perfectly described by the infectious disease model. There is also social discrimination in the obesity epidemic. Social discrimination against obese people plays quite different roles in two cases: on the one hand, when obesity cannot be eliminated, social discrimination can reduce the number of obese people; on the other hand, when obesity is eradicable, social discrimination can cause it to explode.(1)   Materiał and methods: A literature analysis on obesity epidemic was carried out within the Pubmed, Google scholar and Research Gate platform. The following keywords were used in serach: obesity, epidemy, children, body max index.    Purpose of the work: The aim of the following analysis is to present an obesity as an infectious disease. The steadily increasing percentage of obese people, including children, shows that there is an obesity epidemic. This is the phenomenon of social contagion, which partially explains the concept of homophily, which involves the grouping of people with similar characteristics. Potential explanations are also provided by sharing a living environment with similar access to certain foods and similar opportunities for physical activity, which defines the occurrence of analogous health habits

Energy-carrying wave simulation of the Lonngren-wave equation in semiconductor materials

2021 ◽  
pp. 2150213
Author(s):  
Hülya Durur
Keyword(s):  
Wave Equation ◽  
Traveling Wave ◽  
Energy Transport ◽  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Traveling Wave Solution ◽  
Discussion Section ◽  
Advantages And Disadvantages ◽  
Wave Solutions ◽  
Package Program

In this study, the Lonngren-wave equation, which is physically semiconductor, is taken into consideration. Traveling wave solutions of this equation are presented with generalized exponential rational function method, which is one of the mathematically powerful analytical methods. These solutions are produced in bright (non-topological) soliton and complex trigonometric-type traveling wave solutions. Three-dimensional (3D), 2D and contour graphics are presented with the help of a ready-made package program with special values given to constants in these solutions. The effect of the change in wave velocity on the traveling wave solution showing energy transport is presented with the help of simulation. It is argued that velocity is one of the important factors in wave diffraction. In the results and discussion section, the advantages and disadvantages of the method are discussed.

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