Abstract
This paper is concerned with the nonlinear stability of traveling waves of a delayed monostable epidemic model with quasi-monotone condition. We prove that the traveling wave front is exponentially stable by means of the weighted-energy method and the comparison principle to perturbation in some exponentially weighted $L^{\infty}$ spaces, when the difference between initial data and traveling wave front decays exponentially as $x \to -\infty$, but the initial data can be suitable large in other locations. Finally, we present two examples to support our theoretical results.
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