 SIS model

An SIS model returns recovered hosts directly to susceptibility, so immunity does not accumulate. For homogeneous frequency-dependent transmission, a positive endemic state exists at $I_{\ast }=1-1/{\mathcal{R}}_0$ when ${\mathcal{R}}_0=\beta /\gamma >1$. This epidemiological model is distinct from the galaxy-dynamics abbreviation SIS for a singular isothermal sphere.