Traveling Wave Solutions for a Class of Discrete Diffusive SIR Epidemic Model

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