Frailty variation models for susceptibility and exposure to SARS-CoV-2

Individual variation in susceptibility and exposure is subject to selection by force of infection, accelerating the natural acquisition of immunity, and reducing herd immunity thresholds and epidemic final sizes. This is a manifestation of a wider population phenomenon known as "frailty variation" in demography. Despite this theoretical understanding, public health policies continue to be guided by mathematical models that leave out most of the relevant variation and as a result inflate projected infection burdens. Here we focus on the trajectories of the coronavirus disease (COVID-19) pandemic in England and Scotland. We fit models to series of daily deaths and estimate relevant epidemiological parameters, including coefficients of variation which we find in agreement with direct measurements based on published contact surveys. Our estimates are robust to whether the data series encompass one or two pandemic waves. We conclude that herd immunity thresholds are being reached with a larger contribution of vaccination in Scotland than in England, where naturally acquired immunity is higher. These results are relevant to global vaccination policies.

Herd immunity thresholds for SARS-CoV-2 estimated from unfolding epidemics

Variation in individual susceptibility or frequency of exposure to infection accelerates the rate at which populations acquire immunity by natural infection. Individuals that are more susceptible or more frequently exposed tend to be infected earlier and hence more quickly selected out of the susceptible pool, decelerating the incidence of new infections as the epidemic progresses. Eventually, susceptible numbers become low enough to prevent epidemic growth or, in other words, the herd immunity threshold (HIT) is reached. We have recently proposed a method whereby mathematical models, with gamma distributions of susceptibility or exposure to SARS-CoV-2, are fitted to epidemic curves to estimate coefficients of individual variation among epidemiological parameters of interest. In the initial study we estimated HIT around 25-29% for the original Wuhan virus in England and Scotland. Here we explore the limits of applicability of the method using Spain and Portugal as case studies. Results are robust and consistent with England and Scotland, in the case of Spain, but fail in Portugal due to particularities of the dataset. We describe failures, identify their causes, and propose methodological extensions.

Individual variation in susceptibility or exposure to SARS-CoV-2 lowers the herd immunity threshold

Individual variation in susceptibility and exposure is subject to selection by natural infection, accelerating the acquisition of immunity, and reducing herd immunity thresholds and epidemic final sizes. This is a manifestation of a wider population phenomenon known as "frailty variation". Despite theoretical understanding, public health policies continue to be guided by mathematical models that leave out considerable variation and as a result inflate projected disease burdens and overestimate the impact of interventions. Here we focus on trajectories of the coronavirus disease (COVID-19) pandemic in England and Scotland until November 2021. We fit models to series of daily deaths and infer relevant epidemiological parameters, including coefficients of variation and effects of non-pharmaceutical interventions which we find in agreement with independent empirical estimates based on contact surveys. Our estimates are robust to whether the analysed data series encompass one or two pandemic waves and enable projections compatible with subsequent dynamics. We conclude that vaccination programmes may have contributed modestly to the acquisition of herd immunity in populations with high levels of pre-existing naturally acquired immunity, while being critical to protect vulnerable individuals from severe outcomes as the virus becomes endemic. Graphical Abstract O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=161 SRC="FIGDIR/small/20081893v5_ufig1.gif" ALT="Figure 1"> View larger version (19K): org.highwire.dtl.DTLVardef@aeb87forg.highwire.dtl.DTLVardef@d2c441org.highwire.dtl.DTLVardef@152aeceorg.highwire.dtl.DTLVardef@1526779_HPS_FORMAT_FIGEXP M_FIG C_FIG HighlightsO_LIVariation in susceptibility/exposure responds to selection by natural infection C_LIO_LISelection on susceptibility/exposure flattens epidemic curves C_LIO_LIModels with incomplete heterogeneity overestimate intervention impacts C_LIO_LIIndividual variation lowered the natural herd immunity threshold for SARS-CoV-2 C_LI