Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 103, pp. 1-12.

Title: Travelling waves in the lattice epidemic model
       
Authors: Zhixian Yu (Univ. of Shanghai for Science and Tech., China)
        Rong Yuan  (Beijing Normal Univ., Beijing,  China)

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.
 
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.