We consider a generalized SCIS model where individuals are divided into the three compartments S (healthy and susceptible), C (infected but not just infectious) and I (infectious). Finite waiting times in the compartments yield a system of delay-differential or memory equations and may exhibit oscillatory (Hopf) instabilities of the otherwise stationary endemic state, leading normally to regular oscillations in the form of an attractive limit cycle in the phase space spanned by the compartment rates.

In the present paper our aim is to demonstrate that in the dynamics of delayed SCIS models persistent chaotic attractors can bifurcate from these limit cycles and become accessible if the nonlinear interaction terms fulfill certain basic requirements. Computing the largest Lyapunov exponent we show that chaotic behavior exists in a wide parameter range.

Finally, we discuss a more general system and show that a sudden falloff of the infection rate with respect to increasing infection number may be responsible for the emergence of chaotic time evolution. Such a falloff can describe mitigation measures like wearing masques, individual isolation or vaccination. The model may have a wide range of interdisciplinary applications beyond epidemic spreading for instance in the kinetics of certain chemical reactions.