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Recently, [8] has proposed that heterogeneity of infectiousness (andsusceptibility) across individuals in infectious diseases, plays a major rolein affecting the Herd Immunity Threshold (HIT). Such heterogeneity has beenobserved in COVID-19 and is recognized as overdispersion (or"super-spreading"). The model of [8] suggests that super-spreaders contributesignificantly to the effective reproduction factor, R, and that they are likelyto 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%, incontrast to 67% according to the traditional models [1, 2, 4, 10]. This workfollows 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). Theformer is a personal trait of specific individuals (super-spreaders) and isnullified once those individuals are immune (as in [8]). The latter isevent-based (e.g cultural super-spreading events) and remains effectivethroughout the process, even after the super-spreaders immune. We extend [8]'smodel to account for these two factors, analyze it and conclude that the HIT isvery sensitive to the mix between (1) and (2), and under R_0 = 3 it can varybetween 5% and 67%. Preliminary data from COVID-19 suggests that herd immunityis not reached at 5%. We address operational aspects and analyze the effects oflockdown strategies on the spread of a disease. We find that herd immunity (andHIT) is very sensitive to the lockdown type. While some lockdowns affectpositively the disease blocking and increase herd immunity, others have adverseeffects and reduce the herd immunity.

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