A SEIR model with variable susceptibility or exposure to infection

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 much lower than in homogeneous populations. We find explicit formulas to calculate herd immunity thresholds and stable configuration, and explore variations of the model.