AI and the World's Hard Problems · Mathematics · arXiv · 2026-10-22
Time-periodic solutions of an SIS epidemic model
The study proves the existence of strictly positive, nonstationary time-periodic solutions for the spatially heterogeneous SIS epidemic model with standard incidence. An AI-assisted construction of an unstable endemic equilibrium under the pointwise condition β>γ>0, along a coefficient path that preserves the equilibrium and the pointwise inequalities, yields small-amplitude periodic solutions through center-manifold reduction and a generalized Hopf bifurcation argument. The result shows that pointwise dominance of transmission over recovery does not ensure convergence to equilibrium.