Canard phenomenon for an SIS epidemic model with nonlinear incidence

By using the singular perturbation theory, especially on canard cycles, the canard phenomenon for an SIS epidemic model with nonlinear incidence is investigated. The phenomenon suggests the existence of disease outbreak in the infection transmission. It is proved that the cyclicity of any possible slow-fast cycle is at most two, that is at most two families of hyperbolic limit cycles or at most one family of limit cycles with multiplicity two can bifurcate from the slow-fast cycle by small perturbations. We also indicate the regions in parameter space where the corresponding slow-fast cycle has cyclicity at most one or at most two.