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