<p>The spread of epidemics is profoundly affected by adaptive behavior change in response to perceived infection risks. In this study, we propose an SIS epidemic model that integrates behavioral dynamics driven by imitation process based on the game theory. The model also incorporates a density-dependent factor to represent the efficacy of behavior change and saturated recovery to describe the limitation of medical resources. We theoretically analyze the existence and local stability for all equilibria and examine the global stability of disease-free equilibrium and endemic equilibria under certain thresholds. We further calculate conditions for the occurrence of backward bifurcation and Hopf bifurcation, showing that bistability and periodic oscillations are possible. It is worth noting that in consideration of saturated recovery, the basic reproduction number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(R_0=1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> may not be threshold for disease eradication, which enriches the transmission dynamics. By comparing the model without behavior change or saturation recovery, we obtain that saturation recovery, though insufficient to bring about periodicity, can serve as the trigger for bistability, while combination of behavior change and saturated recovery brings about periodic oscillations. Our findings suggest that enhancing public sensitivity to perceived infection risks and expanding medical resources are critical for mitigating outbreaks.</p>