TRAVELING WAVES FOR A CLASS OF DIFFUSIVE DISEASE-TRANSMISSION MODELS WITH NETWORK STRUCTURES.

In this paper, the necessary and sufficient conditions for the existence of traveling wave solutions are derived for a class of diffusive disease-transmission models with network structures. The existence of traveling semifronts is obtained by Schauder's fixed-point theorem, and these traveling semifronts are shown to be bounded by transforming the boundedness problem into the classification problem of nonnegative solutions to a linear elliptic system on R. To overcome the reducibility problem arising in the proofs, Harnack's inequality for positive supersolutions on R is proved. [ABSTRACT FROM AUTHOR]