Year: 2026
Type: preprint
Abstract: We consider a mathematical model of cell-to-cell infection involving target cells, eclipse-phase cells, infectious cells, and dead cells. The infection mechanism is described by spatially discrete contacts in a continuous spatial domain, which reduces to a two-dimensional lattice dynamical system on a regular lattice. By reformulating the system as a nonlinear integral equation and applying a fixed-point argument, we establish the existence of planar traveling waves propagating in any given direction. Retaining the discrete spatial coupling, we incorporate distributed time delays through kernel functions to account for general eclipse-phase durations and prove the persistence of traveling waves. The framework also applies to nonlocal infection contacts. To further characterize the wave profiles, we approximate the one-dimensional spatial system by a reduced two-variable first-order ODE system. Phase-plane analysis then identifies heteroclinic orbits representing the wave profiles. Numerical simulations corroborate the theoretical results and illustrate the propagation of infection waves.
Source: Research Square
Authors: Yusuke Asai, Shingo Iwami, Yoshihisa Morita
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223209197