The codes also reproduce the Figure 1.(B) of Shaman et al. (2010).Harper (1961) tested airborne virus particles of influenza A for viable survival in the dark at controlled temperature and relative humidity for up to 23 hour after spraying. The 1-h influenza A virus survival data are extracted from the paper and now are stored in humidity pacakge with a dataset name of ivs. In this vignette, the dataset ivs is used to explore the relationship between influenza A virus survival and specific humidity. As specific humidity isn’t provided, we first need to apply functions from humidity package to calculate specific humidity from temperature and relative humidity.
# load humidity package
library(humidity)
# built-in 1-h influenza virus surival data
head(ivs)## T RH PVV Tk Es E rho q
## 1 7.50 24.0 78 280.65 10.38008 249.1219 0.001923341 0.001530702
## 2 7.50 51.0 61 280.65 10.38008 529.3840 0.004087100 0.003256149
## 3 7.50 82.0 70 280.65 10.38008 851.1665 0.006571416 0.005241681
## 4 22.25 21.0 64 295.40 27.21156 571.4428 0.004191522 0.003515398
## 5 22.25 35.0 59 295.40 27.21156 952.4047 0.006985870 0.005867353
## 6 22.25 50.5 29 295.40 27.21156 1374.1839 0.010079613 0.008479141Note that SVP function can calculate saturation vapor pressure per either Clausius-Clapeyron equation or Murray equation. Their results are the same and the default formula is Clausius-Clapeyron, which is consistent with Shaman and Kohn (20009). The default value for parameter p in function SH is one standard atmospheric pressure, i.e. 101,325\(Pa\).
Read in the extracted 1-h influenza A virus survival data and call helper functions to calculate specific humidity. Harper (1961) didn’t give any information on the atmospheric pressure condition under which his experiments were conducted. I assume that he performed the experiments under standard atmospheric pressure.
# tempature in Kelvin
ivs$Tk <- C2K(ivs$T)
# saturation vapor pressure in hPa
ivs$Es <- SVP(ivs$Tk)
# partial water vapor pressure in Pa
ivs$E <- WVP(ivs$RH, ivs$Es)
# absolute humidity in kg/m^3
ivs$rho <- AH(ivs$E, ivs$Tk)
# specific humidity in kg/kg
ivs$q <- SH(ivs$E)
# display data
head(ivs)## T RH PVV Tk Es E rho q
## 1 7.50 24.0 78 280.65 10.38008 249.1219 0.001923341 0.001530702
## 2 7.50 51.0 61 280.65 10.38008 529.3840 0.004087100 0.003256149
## 3 7.50 82.0 70 280.65 10.38008 851.1665 0.006571416 0.005241681
## 4 22.25 21.0 64 295.40 27.21156 571.4428 0.004191522 0.003515398
## 5 22.25 35.0 59 295.40 27.21156 952.4047 0.006985870 0.005867353
## 6 22.25 50.5 29 295.40 27.21156 1374.1839 0.010079613 0.008479141Hinted by Shaman and Kohn (20009) and Shaman et al. (2010), log-linear regression model is applied to describe the relationship between influenza A virus survival and specific humidity.
# log-linear regression of 1-h infuenza A virus survival on specific humididty
loglm <- lm(log(PVV) ~ q, data = ivs)
summary(loglm)##
## Call:
## lm(formula = log(PVV) ~ q, data = ivs)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.49834 -0.13209 0.01414 0.16364 0.36192
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.5249 0.1445 31.323 1.69e-10 ***
## q -121.5782 13.1247 -9.263 6.74e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.281 on 9 degrees of freedom
## Multiple R-squared: 0.9051, Adjusted R-squared: 0.8945
## F-statistic: 85.81 on 1 and 9 DF, p-value: 6.74e-06The log-linear regression model is significant with a \(p\)-value less than 0.0001, indicating that log-linear model can well depict the association of influenza virus survival with specific humidity. But the coefficient estimate for specific humidity is \(-121.5076\), which is too far from the value of \(a = -180\) estimated by Shaman et al. (2010).
The following codes draw the scatter plot of 1-h influenza A virus survival and specific humidity, with regression curve overlapped.
# get fitted value to plot regression curve
ivs$fit.val <- exp(predict(loglm))
ivs <- ivs[with(ivs, order(q)), ]
# plot percentage viable virus vs. specific humidity
par(pty = "s")
plot(x = ivs$q, y = ivs$PVV, col = "red", pch = 3, lwd = 3,
xaxt = "n", yaxt = "n", xlim = c(0, 0.03), ylim = c(0, 100),
xaxs = "i", yaxs = "i", xlab = "", ylab = "",
main = "Regression of Influenza A Virus Survival\n on Specific Humidity")
title(xlab = "Specific Humidity (kg/kg)", ylab = "Percent Viable (%)", mgp = c(2, 1, 0))
# plot regression curve
lines(x = ivs$q, y = ivs$fit.val, lty = "dashed", lwd = 4)
axis(side = 1, at = seq(0, 0.03, by = 0.01), labels = c("0", "0.01", "0.02", "0.03"),
tck = 0.01, padj = -0.5)
axis(side = 2, at = seq(0, 100, by = 20), tck = 0.01, las = 2, hadj = 0.5)
axis(side = 3, at = seq(0, 0.03, by = 0.01), labels = FALSE, tck = 0.01)
axis(side = 4, at = seq(0, 100, by = 20), labels = FALSE, tck = 0.01)
legend(0.011, 95, legend = c("1 Hour Viability", "p < 0.0001"), pch = c(3, NA),
col = c("red", "black"), lty = c(NA, "dashed"), lwd = c(3, 4), seg.len = 5) The codes also reproduce the Figure 1.(B) of Shaman et al. (2010).