{ const chart1 = vl.markCircle().title("Infectivty Share vs Percentile") // Make a scatter chart .data(data_percentiles) .encode( vl.x().fieldQ("p").title('percentile').axis({format: ".0%"}), vl.y().fieldQ("infectivityshare").title('infectivityshare'), vl.tooltip(["infectivityshare","x"]) ) return md` ### Infectivity comparisons The previous figure shows the "infectivity" across ${numPts} representative people. The figures below show the infectivity share. The individual infectivity of all the people are added up to get total infectivity. The share is the proportion of the total infectivity. ${ await vl.markCircle().title("Infectivty Share vs Viral Concentration") // Make a scatter chart .data(data_percentiles) .encode( vl.x().fieldQ("x").scale({type: 'log'}).title('RNA concentration [GE/vol]').axis({format: ".2e"}), vl.y().fieldQ("infectivityshare").title('Infectivity Share'), vl.tooltip(["infectivityshare","x"]) ).render() } ${await vl.layer(chart1).render()} The individual infectivity is assumed to be proportional to the concentration of the virus in a PCR sample, as done in [G. Buonanno et al. (Aug 2020)](https://doi.org/10.1016/j.envint.2020.105794), [G. Buonanno et al. (Dec 2020)](https://doi.org/10.1016/j.envint.2020.106112), and in the Jimenez covid risk calculator [link1, google spreadsheet original](http://tinyurl.com/covid-estimator) and [link2, Observable Notebook](https://observablehq.com/@chonghorizons/covid-individual-event-risk-calculator-v0-2) In particular, Buonanno et al write: > In the present paper we have considered an average c_v value of 10^7 copies/mL. after finding a range of > researchers have recently found c_v values in the range 10^3-10^11 copies mL−1 Though 10^7 may represent the median viral concentration and they are careful to state their assumption, this analysis of the logNormal distribution suggests that the median value may underestimate infectivity. ### Adequate protection Specifically, one might choose a set of preventative measures (ventilation, masks, etc) that protects against the median concentration, currently set at ${(10**logCenter).toExponential(2)}. However, this may not protect against quanta in the edge cases. * 10% of cases will have ${(log10NormalInstance.percentile(0.9)/(10**logCenter)).toLocaleString(undefined, {maximumSignificantDigits: 2})} times the median quanta. _{^{concentrations of at least 10^${Math.log10(log10NormalInstance.percentile(0.9)).toFixed(2)} or ${log10NormalInstance.percentile(0.9).toLocaleString(undefined, {maximumSignificantDigits: 3})}}} * 5% of cases will have ${(log10NormalInstance.percentile(0.95)/(10**logCenter)).toLocaleString(undefined, {maximumSignificantDigits: 2})} times the median quanta. _{^{concentrations of at least 10^${Math.log10(log10NormalInstance.percentile(0.95)).toFixed(2)} or ${log10NormalInstance.percentile(0.95).toLocaleString(undefined, {maximumSignificantDigits: 3})}}} * 1% of cases will have ${(log10NormalInstance.percentile(0.99)/(10**logCenter)).toLocaleString(undefined, {maximumSignificantDigits: 2})} times the median quanta. _{^{concentrations of at least 10^${Math.log10(log10NormalInstance.percentile(0.99)).toFixed(2)} or ${log10NormalInstance.percentile(0.99).toLocaleString(undefined, {maximumSignificantDigits: 3}) }}} ### Infectivity Shares The top 10% of people carry the bulk of the infectivity/viral concentration. * The top 5% have an infectivity share of ${data_percentiles.reduce( (acc,row) => { if (row.p<0.95) return acc; return acc+ row.infectivityshare; },0).toLocaleString(undefined, { style: "percent", maximumSignificantDigits: 3 })} * The top 10% have an infectivity share of ${data_percentiles.reduce( (acc,row) => { if (row.p<0.90) return acc; return acc+ row.infectivityshare; },0).toLocaleString(undefined, { style: "percent", maximumSignificantDigits: 3 })} ` }