Sampling and Sequencing Simulator

Each time the tool samples, it uses a Poisson approximation of binomial sampling to determine how many sick people are in the sample. Similarly, each time it sequences, it uses a Poisson approximation of binomial sampling to determine how many sequencing reads are obtained for the pathogen of interest. Detection is modeled as happening when a specified threshold number of sequencing reads that match a specific portion of the target genome is accumulated.

The tool assumes that sequencing reads are moderately unevenly distributed along the pathogen's genome, following the coverage distribution we observe for SARS-CoV-2 in unpublished MU data.

The tool simulates many times (1,000 by default) and charts the range of cumulative incidences observed. Any outcomes where the cumulative incidence is over 30% are marked as a failure by showing a "0"; on the chart. The simulation is not correct for high cumulative incidence, as it only models the initial exponential stage of the epidemic.

Certain values allow you to specify how much noise to add to the model. The noise is generated once per simulation. For the inputs marked "CV" the noise is normally; for ones marked "CV_g" the noise is lognormally distributed. The higher the CV you set, the more uncertainty will be introduced into the simulation, generally causing the low-percentile outputs to be more optimistic and the high-percentile outputs to be more pessimistic.

If we're starting with a set of individual-level relative abundances we multiply them by lognormally distributed noise with μ=0 and σ=σ_g. This noise shifts all provided values in the same direction to represent our uncertainty about whether these relative abundances are systematically too high or low. For example, if in one of the 1,000 simulations our lognormal draw gives us a noise value of is 0.7 and the provided values are 1e-5 and 1e-6, for that simulation each time someone is sick we'll pick one of 7e-6 and 7e-7.

On the other hand, if we're starting with an imported RA_i(1%) distribution we draw from the distribution once for each simulation. For example, if in one of the 1,000 simulations our RA_i(1%) draw gives us 1e-7, then when 1% of people became infected in the last week we'll draw the number of sequencing reads that match the pathogen from a Poisson distribution with a mean of the total number of sequencing reads times 1e-7.

Real epidemics don't grow perfectly exponentially. Early on individual infection events can have a large contribution, such as with superspreader events. This tool assumes simple exponential growth.

Real epidemics would happen to progress faster in some locations and slower in others. If you're sampling at mutiple sites you should see an epidemic be farther ahead in some places than others. This tool assumes the epidemic grows equally quickly at each site, which underestimates the value of running multiple sites.

Real epidemics fall below exponential, even if they're spreading unnoticed, once there's an appreciable number of succeptible people. This tool only simulates the early portion of the curve, where exponential is a good approximation. In practice this is a minimal limitation, because we're really only concerned with scenarios that would let us flag a pandemic before too many people had been infected.

For very substantial efforts, with very deep sequencing across many sites, a real detection system would start to see economies of scale. We don't model this, and instead assume linear cost per site.