In one of many attempts to better understand the correlation between social distancing and new COVID-19 infections, the Signer Lab at the University of California San Diego had reported that a single infected person on average may lead to a total of 2.5, 15 or 406 COVID-19 infections over a one moth period.

a) Suppose that starting from a single infected person and without any social distancing measures in place, the number of new infections over a 5-day period follows a uniform distribution between 0 and 5 (this is consistent with the frequently stated average transmissibility, attack rate or reproduction number R0 of 2.5). Develop a simulation model for the total number of resulting COVID-19 infections over a one-moth period (i.e., 30 days). Give its average and show its distribution using a histogram or another suitable visualization. You may assume that an infected individual will unknowingly spread COVID-19 over a five-day incubation period only; after this period, the individual will begin to develop symptoms, immediately self quarantine, and no longer pose a threat.

b) How will your answers change if social exposure can be reduced by 50% or 75% respectively?

You may assume a direct linear correlation of social interactions and R0; e.g., if social exposure is reduced by 50% (or 75%), R0 will follow a uniform distribution of only up to 2.5 (or 1.25) with a mean of 1.25 (or 0.625). Can you confirm the findings of the Signer Lab, and why or why not?