%0 Journal Article %T Traveling waves for a diffusive SIR model with delay and nonlinear incidence %A Wang, Yanmei %A Liu, Guirong %A Zhao, Aimin %J Journal of Nonlinear Sciences and Applications %D 2018 %V 11 %N 12 %@ ISSN 2008-1901 %F Wang2018 %X This paper is concerned with the existence and non-existence of traveling wave solutions for a diffusive SIR model with delay and nonlinear incidence. First, we construct a pair of upper and lower solutions and a bounded cone. Then we prove the existence of traveling wave by using Schauder's fixed point theorem and constructing a suitable Lyapunov functional. The nonexistence of traveling wave is obtained by two-sided Laplace transform. Moreover, numerical simulations support the theoretical results. Finally, we also obtain that the minimal wave speed is decreasing with respect to the latent period and increasing with respect to the diffusion rate of infected individuals. %9 journal article %R 10.22436/jnsa.011.12.03 %U http://dx.doi.org/10.22436/jnsa.011.12.03 %P 1313--1330