On the asymptotic behaviour of traveling wave solution for a discrete diffusive epidemic model

A recent paper [Y.-Y. Chen, J.-S. Guo, F. Hamel, Traveling waves for a lattice dynamical system arising in diffusive endemic model, Nonlinearity, 30 (2017), 2334-2359] presented discrete Kermack-McKendrick epidemic and the authors proved existence of traveling wave solutions connecting disease-free equilibrium to equilibrium. However, boundary asymptotic behavior converge at $ +\infty is still an open problem. In this paper, we investigate above problem completely solve it by constructing suitable Lyapunov functional employing Lebesgue dominated convergence theorem.