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

2019/02/04 by Romain Ducasse, Ducasse, Romain
Mathematics · Medicine · #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis

paper · doi:10.48550/arxiv.1902.01072

openalex publication_date 2019/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study some anisotropic heterogeneous nonlinear integral equations arising in epidemiology. We focus on the case where the heterogeneities are spatially periodic. 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", and we provide a formula for the admissible speeds. In a third part, we apply our results to a spatial heterogeneous SIR model.

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