Resumen de Traveling Wave Solution with the Critical Speed for a Diffusive Epidemic System with Spatio-Temporal Delay

Zaili Zhen, Jingdong Wei, Jiangbo Zhou, Minjie Dong, Lixin Tian

• The existence of a critical traveling wave solution for a reaction-diffusion epidemic system with spatio-temporal delay is established, whose existence of super-critical traveling wave solutions is obtained in [Z. Zhen et al., Math. Method. Appl. Sci.

  41 (2018) 7074-7098]. Meanwhile, the non-existence of traveling waves with nonpositive speeds are derived. Two open problems left in the paper [Z. Zhen et al., Math.

  Method. Appl. Sci. 41 (2018) 7074-7098] are solved. Moreover, some properties of super-critical traveling waves are improved.