  We study a SEIR model considered by Gomes et al. \cite{Gomes2020} and Aguas
et al. \cite{Aguas2020} where different individuals are assumed to have
different levels of susceptibility or exposure to infection. Under this
heterogeneity assumption, epidemic growth is effectively suppressed when the
percentage of population having acquired immunity surpasses a critical level -
the herd immunity threshold - that is lower than in homogeneous populations. We
find explicit formulas to calculate herd immunity thresholds and stable
configuration, and explore extensions of the model.
