Fig. 2.

TCI threshold (dot-dashed), long-term heterogeneous HIT (solid), and homogeneous HIT (dotted) for various values of $R_0$ (x axis). HIT (solid line) is determined by persistent heterogeneity. The corresponding immunity factor ${\lambda }_{\infty }\approx 2$ was estimated from Eq. 20 assuming strong short-term overdispersion (${\chi }^{*}\ll 1$) and the exponential distribution of $\alpha$ ($\eta =1$). For transient behavior, ${\lambda }_{\mathrm{e}\mathrm{ff}}\approx 4$ is assumed based on analysis of empirical data for COVID-19 epidemic in select locations.