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

• Ducasse Romain

• Heterogeneous models
• Epidemic Model
• SIR model
• Traveling waves
• Anisotropic equations
• Threshold phenomenon
• Nonlinear integral equations
• Integro-differential systems

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.