Travelling waves in the lattice epidemic model

Abstract

In this article, we establish the existence and nonexistence of travelling waves for a lattice non-monotone integral equation which is an epidemic model. Moreover, the wave is either convergent to the positive equilibrium or oscillating on the positive equilibrium at positive infinity, and has the exponential asymptotic behavior at negative infinity. For the non-monotone case, the asymptotic speed of propagation also coincides with the minimal wave speed.

Keywords

• Travelling waves
• Schauder's fixed point theorem
• non-monotone integral equation
• oscillatory solution