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Traveling waves for SIR model on two-dimensional lattice

Ran Zhang, Shunchang Su, Xue Ren

Abstract

In this study, we investigate the existence of traveling wave solutions for a SIR model on two-dimensional lattice. The existence of traveling waves is established within the framework of upper and lower solutions and the Schauder fixed-point theorem. Moreover, we construct a Lyapunov functional to analyze the asymptotic behavior of the traveling wave solutions. This is a challenging task due to the two-dimensional lattice structure.

Traveling waves for SIR model on two-dimensional lattice

Abstract

In this study, we investigate the existence of traveling wave solutions for a SIR model on two-dimensional lattice. The existence of traveling waves is established within the framework of upper and lower solutions and the Schauder fixed-point theorem. Moreover, we construct a Lyapunov functional to analyze the asymptotic behavior of the traveling wave solutions. This is a challenging task due to the two-dimensional lattice structure.
Paper Structure (7 sections, 13 theorems, 127 equations)

This paper contains 7 sections, 13 theorems, 127 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Construction of upper and lower solutions
  4. Existence of traveling wave solution
  5. Truncated problem
  6. Existence of Traveling Wave Solutions
  7. Nonexistence of Traveling Wave Solutions

Key Result

Lemma 2.1

Let $\Re_{0}>1.$ There exist $c^*>0$ and $\lambda^*>0$ such that Furthermore,

Theorems & Definitions (23)

  • Lemma 2.1
  • Lemma 2.2
  • Lemma 2.3
  • proof
  • Lemma 2.4
  • proof
  • Lemma 2.5
  • proof
  • Lemma 3.1
  • proof
  • ...and 13 more