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We study a diffusive SIS epidemic model with the mass-action transmissionmechanism and show, under appropriate assumptions on the parameters, theexistence of multiple endemic equilibria (EE). Our results answer some openquestions on previous studies related to disease extinction or persistence when$\mathcal{R}_0<1$ and the multiplicity of EE solutions when $\mathcal{R}_0>1$.Interestingly, even with such a simple nonlinearity induced by the mass-action,we show that the diffusive epidemic model may have an S-shaped or backwardbifurcation curve of EE solutions.

Multiplicity of endemic equilibria for a diffusive SIS epidemic model with mass-action