#10 · Systems biology

Reduced models expose oscillations in epidemics and travelling waves in tissue

The three preprints share a reduction strategy in which a complex nonlinear model is replaced by a tractable structural or approximate form that exposes emergent spatiotemporal behavior. The multi-strain epidemic framework resolves severe algebraic complexity analytically to map self-sustained oscillations. The SVEIR influenza study calibrates an ODE model to influenza data and extends it with a diffusion-chemotaxis PDE including fear effects, analyzed via an IMEX numerical scheme. The tissue competition study combines simulations with a quasi-stationary approximation to show travelling waves with winner-takes-all speeds. This thread is dominant rather than universal: only the multi-strain framework achieves complete analytical resolution, while the others rely on numerical schemes or approximation. What is new is the explicit use of minimal analytical or approximate structure to predict oscillations and waves across epidemic and tissue settings.