Uniqueness of epidemic waves in a host-vector disease model

Xu, Zhaoquan; Xiao, Dongmei

doi:10.1090/proc/14043

Uniqueness of epidemic waves in a host-vector disease model
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by Zhaoquan Xu and Dongmei Xiao PDF

Proc. Amer. Math. Soc. 146 (2018), 3875-3886 Request permission

Abstract:

A diffusive integro-differential equation which serves as a model for the evolution of a host-vector epidemic was extensively studied in literature. The traveling wave solutions of this model describe the spread of the disease from a disease-free state to an infective state, which are epidemic waves. It is a challenging problem if epidemic waves with the minimal propagation speed are unique up to translation. In this paper, we establish the uniqueness of all epidemic waves with any an admissible wave speed by the sliding method and solve this challenging problem completely.

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