A Rigorous Computer-Assisted Verification of Horseshoe Chaos in a Seasonally Forced SEIR Epidemic Model

The current famous topological horseshoe theory is applied to an SEIR epidemic model with sinusoidally varying contact rate. For the first time, a rigorous computer-assisted verification of the existence of horseshoe chaos in this SEIR model is presented, which implies that chaos does exist from a theoretical and mathematical viewpoint other than the purely numerical computations viewpoint. By virtue of the Poincare map, an appropriate Poincare section is chosen to obtain the corresponding Poincare map, which is proved to be semi-conjugate to 2-shift map. This implies that the SEIR epidemic system has positive topological entropy no less than log2, and thus is definitely chaotic.