| Abstract: |
| Some {\it in vitro} experiments have observed the propagation of viral infection through cell-to-cell contact. Motivated by this phenomenon, we consider a cell-to-cell infection model consisting of variables representing the concentrations of target cells, eclipse-phase cells, infectious cells, and dead cells. The model describes the spread of infection through spatially discrete coupling between neighboring infectious and target cells. Numerical simulations demonstrate the emergence of traveling waves representing the propagation of the infectious state. We establish the existence of such traveling waves by reformulating the system as a nonlinear integral equation and applying a fixed-point argument. We also show that an integro-differential formulation of the model admits traveling wave solutions.This talk is based on the work of Asai-Iwami-Morita (2026). |
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