A modified nonlinear incidence rate in an SIS epidemic model was investigated. When a new disease emerged or an old one resurged, the infectivity was initially high. Subsequently, the psychological effect attenuated the infectivity. Eventually, due to the crowding effect, the infectivity reached a saturation state. The nonlinearity of the functional form of the infection incidence was modified to enhance its biological plausibility. The stability of the associated equilibria was examined, and the basic reproduction number and the critical value that governed the dynamics of the model were deduced. Bifurcation analyses were presented, encompassing backward bifurcation, saddle-node bifurcation, Bogdanov-Takens bifurcation of codimension two, and Hopf bifurcation. Numerical simulations were conducted to validate our findings.