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We study the spread of disease in an SIS model. The model considered is atime-varying, switched model, in which the parameters of the SIS model aresubject to abrupt change. We show that the joint spectral radius can be used asa threshold parameter for this model in the spirit of the basic reproductionnumber for time-invariant models. We also present conditions for persistenceand the existence of periodic orbits for the switched model and results for astochastic switched model.

Stability Criteria for SIS Epidemiological Models under Switching Policies