This paper is concerned with the conditions of existence and nonexistence of traveling wave solutions (TWS) for a class of discrete diffusive epidemic model. We find that the existence of TWS is determined by the so-called basic reproduction number and the critical wave speed: When the basic reproduction number \(\mathfrak {R}_0>1\), there exists a critical wave speed \(c^*>0\), such that for each \(c \ge c^*\) the system admits a nontrivial TWS and for \(c<c^*\) there exists no nontrivial TWS for the system. In addition, the boundary asymptotic behavior of TWS is obtained by constructing a suitable Lyapunov functional and employing Lebesgue dominated convergence theorem. Finally, we apply our results to two discrete diffusive epidemic models to verify the existence and nonexistence of TWS.

研究了一类离散扩散流行病模型的行波解（TWS）存在和不存在的条件。我们发现TWS的存在是由所谓的基本再现数和临界波速决定的：当基本再现数\（\ mathfrak {R} _0> 1 \）时，存在临界波速\（c ^ *> 0 \），这样，对于每个\（c \ ge c ^ * \），系统都会接受一个非平凡的TWS，对于\（c <c ^ * \）该系统没有不平凡的交易平台。此外，通过构造合适的Lyapunov泛函并使用Lebesgue为主的收敛定理，获得了TWS的边界渐近行为。最后，我们将我们的结果应用于两个离散的扩散流行模型，以验证TWS的存在和不存在。