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Bifurcation Chaos"],"published-print":{"date-parts":[[2023,12,30]]},"abstract":" In this study, we extend an SIS epidemic model by introducing a piecewise smooth incidence rate. By assuming that the demographic parameters are much smaller than the disease-related ones, the proposed model is converted to a slow\u2013fast system. Utilizing the geometrical singular perturbation theory and entry-exit function, we prove the coexistence of two relaxation oscillations surrounding the unique positive equilibrium of the model. Numerical simulations are performed to verify our theoretical results. 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