Confusion about coronavirus testing and the role of testing capacity

2020 March 30
by Daniel Lakeland

Here’s some code to simulate a process whereby we saturate testing capacity… First the graphs:

Confirmed cases (blue) follows the real cases (red) so long as the cases per day are below the maximum… once we saturate, the green line increases linearly, and so does the blue line…
Green line (tests) parallels the blue (positive tests), as we saturate
library(ggplot2)

t = seq(1,40)
realcases = 100*exp(t/4)
realincrement = diff(c(0,realcases))

testseekers = rnorm(NROW(realincrement),4,.25)*realincrement

maxtests = 20000

## now assume that you test *up to* 20k people. if more people are
## seeking tests, you test a random subset of the seekers
## getting a binomial count of positives for the given frequency

ntests = rep(0,NROW(t));
ntests[1] = 100;
confinc = rep(0,NROW(t));
confinc[1] = 100;
for(i in 2:(NROW(t)-1)){
    if(testseekers[i] < maxtests){
        confinc[i] = realincrement[i]
        ntests[i] = testseekers[i]
    }
    else if(testseekers[i] > maxtests){
        confinc[i] = min(realincrement[i],rbinom(1,maxtests,realincrement/testseekers))
        ntests[i] = maxtests
    }
}

cumconf = cumsum(confinc)
cumtests = cumsum(ntests)

ggplot(data.frame(t=t,conf=cumconf,nt=cumtests,real=realcases))+geom_line(aes(t,cumconf),color="blue")  + geom_line(aes(t,nt),color="green")+ geom_line(aes(t,real),color="red") +coord_cartesian(xlim=c(0,35),ylim=c(0,400000));


ggplot(data.frame(t=t,conf=cumconf,nt=cumtests,real=realcases))+geom_line(aes(t,log(cumconf)),color="blue") + geom_line(aes(t,log(nt)),color="green")+ geom_line(aes(t,log(real)),color="red") +coord_cartesian(xlim=c(0,30),ylim=c(0,log(400000)));

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