Abstract:

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 semi-fronts is obtained by Schauder’s fixed-point theorem and these traveling semi-fronts are shown to be bounded by transforming the boundedness problem into the classification problem of non-negative solutions to a linear elliptic system on . To overcome the reducibility problem arising in the proofs, a Harnack’s inequality for positive supersolutions on is proved. This is joint work with Adrian Lam and Tianran Zhang.