In this paper, the full information about the existence and nonexistence of a time-periodic traveling wave solution of a reaction–diffusion Zika epidemic model with seasonality, which is non-monotonic, is investigated. More precisely, if the basic reproduction number, denoted by \(R_{0}\), is larger than one, there exists a minimal wave speed \(c^* > 0\) satisfying for each \(c > c^*\), the system admits a nontrivial time-periodic traveling wave solution with wave speed c, and for \(c<c^*\), there exist no nontrivial time-periodic traveling waves such that if \(R_0 \leqslant 1\), the system admits no nontrivial time-periodic traveling waves.

本文研究了非单调的季节性反应扩散寨卡流行模型的时间周期行波解是否存在的完整信息。更准确地说，如果基本再生数（用\(R_{0}\)表示）大于 1，则存在满足每个\(c > c^* 的最小波速\(c^* > 0\) \)，系统承认波速为c 的非平凡时间周期行波解，并且对于\(c<c^*\)，不存在非平凡时间周期行波，使得如果\(R_0 \leqslant 1\ )，系统不允许存在非平凡的时间周期行波。