Abstract
In this article, the well-posedness of the initial value problem, the existence of traveling wavefronts and the asymptotic speed of propagation for a SIR epidemic model with stage structure and nonlocal response are studied. We further show that the minimum wave speed in fact coincides with the asymptotic speed of propagation.
Highlights
Gourley and Kuang [12] introduced a diffusive population model with stage structure: ⎧ ⎨ ∂1 ∂ = ⎩ ∂2 + ∂2 1 1∂ 2 2− 1 − e− ∫ √1 e−
The purpose of our work is to study the existence of traveling wavefronts and the asymptotic speed of propagation for the epidemic model (1)
We show that the minimum wave speed is the asymptotic speed of propagation
Summary
SIR epidemic model, stage structure; nonlocal response, asymptotic speed of propagation, traveling wavefront. The purpose of our work is to study the existence of traveling wavefronts and the asymptotic speed of propagation for the epidemic model (1). To the best of our knowledge, it is the first work that the existence of traveling wavefronts and the asymptotic speed of propagation for a diffusive SIR model with stage structure and nonlocal effect described by (1) has been done.
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