Super-Spreaders Out, Super-Spreading In: The Effects of Infectiousness Heterogeneity and Lockdowns on Herd Immunity

Recently, [8] has proposed that heterogeneity of infectiousness (and susceptibility) across individuals in infectious diseases, plays a major role in affecting the Herd Immunity Thresh-old (HIT). Such heterogeneity has been observed in COVID-19 and is recognized as overdis-persion (or “super-spreading”). The model of [8] suggests that super-spreaders contribute significantly to the effective reproduction factor, R , and that they are likely to get infected and immune early in the process. Consequently, under R 0 ≈ 3 (attributed to COVID-19), the Herd Immunity Threshold (HIT) is as low as 5%, in contrast to 67% according to the traditional models [1, 2, 4, 10]. This work follows up on [8] and proposes that heterogeneity of infectiousness (susceptibility) has two “faces” whose mix affects dramatically the HIT: (1) Personal-Trait- , and (2) Event-Based- Infectiousness (Susceptibility). The former is a personal trait of specific individuals ( super-spreaders ) and is nullified once those individuals are immune (as in [8]). The latter is event-based (e.g cultural super-spreading events) and remains effective throughout the process, even after the super-spreaders immune. We extend [8]’s model to account for these two factors, analyze it and conclude that the HIT is very sensitive to the mix between (1) and (2), and under R 0 ≈ 3 it can vary between 5% and 67%. Preliminary data from COVID-19 suggests that herd immunity is not reached at 5%. We address operational aspects and analyze the effects of lockdown strategies on the spread of a disease. We find that herd immunity (and HIT) is very sensitive to the lock-down type. While some lockdowns affect positively the disease blocking and increase herd immunity, others have adverse effects and reduce the herd immunity.