Threshold phenomenon and traveling waves for heterogeneous integral equations and epidemic models

Abstract : We study anisotropic heterogeneous nonlinear integral equations arising in epidemiology. We focus on the case where the heterogeneities have a periodic structure. In the first part of the paper, we show that the equations we consider exhibit a threshold phenomenon. In the second part, we study the existence and non-existence of traveling waves. The results we derive apply in particular to spatially periodic integro-differential SIR systems.
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https://hal.archives-ouvertes.fr/hal-02004866
Contributor : Romain Ducasse <>
Submitted on : Saturday, February 2, 2019 - 6:00:07 PM
Last modification on : Monday, March 4, 2019 - 2:04:22 PM
Long-term archiving on : Friday, May 3, 2019 - 4:07:08 PM

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  • HAL Id : hal-02004866, version 1
  • ARXIV : 1902.01072

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Romain Ducasse. Threshold phenomenon and traveling waves for heterogeneous integral equations and epidemic models. 2019. ⟨hal-02004866⟩

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