  In this paper, the existence of a non-trivial, positive and bounded critical
traveling wave solution of a diffusive disease model, whose reaction system has
infinity many equilibria, is obtained for the first time. This gives an
affirmative answer to an open problem left in [X. Wang, H. Wang, J. Wu,
Traveling waves of diffusive predator-prey systems: disease outbreak
propagation, Discrete Contin. Dyn. Syst. Ser. A 32 (2012) 3303-3324]. Our
result shows that the critical traveling wave in this model is a mixed of front
and pulse type.
