This paper introduces the global dynamics of an SIS model with bilinear incidence rate and saturated treatment function. The\ntreatment function is a continuous and differential function which shows the effect of delayed treatment when the rate of treatment\nis lower and the number of infected individuals is getting larger. Sufficient conditions for the existence and global asymptotic stability\nof the disease-free and endemic equilibria are given in this paper. The first Lyapunov coefficient is computed to determine various\ntypes of Hopf bifurcation, such as subcritical or supercritical. By some complex algebra, the Bogdanov-Takens normal form and\nthe three types of bifurcation curves are derived. Finally, mathematical analysis and numerical simulations are given to support our\ntheoretical results.
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