Threshold phenomenon and traveling waves for heterogeneous integral equations and epidemic models. (May 2022)

• Record Type: Journal Article
• Authors: Ducasse, Romain
• Is Part Of: Nonlinear analysis. Volume 218(2022)
• Publication Date: 2022-05
• Subjects: 45M05 -- 45M15 -- 35R09 -- 35B40 -- 92D30; Nonlinear integral equations -- Integro-differential systems -- Epidemiology -- SIR models -- Threshold phenomenon -- Traveling waves -- Anisotropic equations -- Heterogeneous models; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.112788
• Languages: English
• ISSNs: 0362-546X

Abstract

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.