Electron. J. Diff. Equ., Vol. 2010(2010), No. 103, pp. 1-12.

Travelling waves in the lattice epidemic model

Zhixian Yu, Rong Yuan

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.

Submitted May 10, 2010. Published July 28, 2010.
Math Subject Classifications: 35C07, 35R09, 34A33.
Key Words: Travelling waves; Schauder's fixed point theorem; non-monotone integral equation; oscillatory solution.

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Zhixian Yu
College of Science
University of Shanghai for Science and Technology
Shanghai 200093, China
email: yuzx@mail.bnu.edu.cn
Rong Yuan
School of Mathematical Sciences
Beijing Normal University
Beijing 100875, China
email: ryuan@bnu.edu.cn

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