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Existence and asymptotic behavior of traveling waves in a host-vector epidemic model
Xijun Deng,Aiyong Chen
Keywords:Host-vector epidemic model, traveling waves, linear chain technique, geometric singular perturbation theory
Abstract:
      In this paper, we are concerned with a diffusive host-vector epidemic model with a nonlocal spatiotemporal interaction. When the delay kernel takes some special form, by employing linear chain techniques and geometric singular perturbation theory, we establish the existence of travelling front solutions connecting the two spatially uniform steady states for sufficiently small delays. Furthermore, by employing standard asymptotic theory, we also obtain the asymptotic behavior of traveling wave fronts of this model.