Traveling Waves for a Class of Diffusive Disease-Transmission Models with Network Structures.
SIAM Journal on Mathematical Analysis(2018)
摘要
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 $\mathbb{R}$.To overcome the reducibility problem arising in the proofs, Harnack's inequality for positive supersolutions on $\mathbb{R}$ is proved.
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关键词
disease-transmission models,traveling wave,classification problem,rescaling method,Harnack's inequality
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