Persistent heterogeneity not short-term overdispersion determines herd immunity to COVID-19

Tkachenko, Alexei V.; Maslov, Sergei; Elbanna, Ahmed; Wong, George N.; Weiner, Zachary J.; Goldenfeld, Nigel

doi:10.2172/1659688

Cited by 19 publications

(26 citation statements)

References 29 publications

(68 reference statements)

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“…Our results contrasting mechanistic variable exposure and susceptibility models are in line with theoretical studies, which also indicate that models incorporating heterogeneity in exposure have more pronounced effects on HITs than models incorporating heterogeneity in susceptibility, assuming comparable continuous distributions of exposure and susceptibility [4, 6]. Tkachenko et al showed that the HIT = 1 − (1 /R 0 ) (1 /λ ) , where λ is either 1 + CV 2 for variable susceptibility models or 1 + CV 2 (2 + γ s CV ) / (1 + CV 2 ) for variable exposure models, and CV is the coefficient of variation and γ s is the skewness for the exposure distribution [6]. We calculated CV and skewness using the susceptibility and activity ratios and substituted those values into the HIT formula, which is an approximation because our exposure and susceptibility distributions are discrete; nonetheless, the approximations result in similar HIT curves to the simulation results (Supplementary Figure 4).…”

Section: Supplementary Informationsupporting

confidence: 85%

“…However, population homogeneity is an unrealistic assumption, and models incorporating hetero-geneity in social exposure and infection susceptibility (defined as the probability of infection given exposure) generally result in lowered HITs [2–6]. The key idea behind these models is that sub-populations important for epidemic spread (i.e., those with substantially increased susceptibility or exposure) become infected – and thus develop immunity – early on in an epidemic’s course.…”

Section: Introductionmentioning

confidence: 99%

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Modeling the impact of racial and ethnic disparities on COVID-19 epidemic dynamics

Kévin

Menkir

Kissler

et al. 2021

Preprint

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The impact of variable infection risk by race and ethnicity on the dynamics of SARS-CoV-2 spread is largely unknown. Here, we fit structured compartmental models to seroprevalence data from New York State and analyze how herd immunity thresholds (HITs), final sizes, and epidemic risk changes across racial and ethnic groups. A proportionate mixing model reduced the overall HIT, but more realistic levels of assortative mixing increased the threshold. Across all models, the burden of infection fell disproportionately on minority populations: in an assortative mixing model fit to Long Island census data, 80% of Hispanics or Latinos were infected when the HIT is reached compared to 33% of non-Hispanic whites. Our findings, which are meant to be illustrative and not best estimates, demonstrate how racial and ethnic disparities can impact epidemic trajectories and result in a dis-proportionate distribution of the burden of SARS-CoV-2 infection.

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Section: Supplementary Informationsupporting

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Modeling the impact of racial and ethnic disparities on COVID-19 epidemic dynamics

Kévin

Menkir

Kissler

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Super-spreading can also have a social component, exemplified by highly social individuals, who come into contact with a large number of people in a limited time-frame. However, such individuals would also be super receivers , a trait which impacts the epidemic even in the absence of mitigation [20, 25]. In any case, ability as well as opportunity is necessary for superspreading to occur.…”

Section: Figmentioning

confidence: 99%

Superspreaders provide essential clues for mitigation of COVID-19

Nielsen

Sneppen

2020

Preprint

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Although COVID-19 has caused severe suffering globally, the efficacy of non-pharmaceutical interventions has been greater than typical models have predicted. Meanwhile, evidence is mounting that the pandemic is characterized by superspreading. Capturing this phenomenon theoretically requires modeling at the scale of individuals. Using a mathematical model, we show that superspreading represents an Achilles' heel of COVID-19. It drastically enhances mitigations which reduce the personal contact number, and social clustering ("social bubbles") increases this effect.

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“…The model of [8] is based on the observation [9, 11, 13] that the epidemic spread network is not homogeneous, where distinct individuals are infectious (likely to infect others) and susceptible (likely to become infected themselves) in various degrees. The heterogeneity of these values among individuals is recognized as overdispersion or super-spreading ( super-spreaders are a class of individuals whose secondary infection rate is very high [5]).…”

Section: Introductionmentioning

confidence: 99%

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

Tavori

Levy

2021

Preprint

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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 R0 ≈ 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 R0 ≈ 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.

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Persistent heterogeneity not short-term overdispersion determines herd immunity to COVID-19

Cited by 19 publications

References 29 publications

Modeling the impact of racial and ethnic disparities on COVID-19 epidemic dynamics

Modeling the impact of racial and ethnic disparities on COVID-19 epidemic dynamics

Superspreaders provide essential clues for mitigation of COVID-19

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

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