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 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.