Lies, Gosh Darn Lies, and Not Enough Good Statistics: Why Epidemic Model Parameter Estimation Fails

Daniel E Platt; Laxmi E Parida; Pierre Zalloua

The rate of infection for a susceptible individual depends on the probability that an infectious viral load is transferred, multiplied by the rate of encounters a susceptible individual has. The encounters can involve: other susceptible individuals, or symptomatic infectious people, which as a group tends to be isolated with a corresponding depressed rate of encounters , and undetected asymptomatic infectious people whose interaction rate is substantially higher, subject to social distancing regulations. The fraction of infectious symptomatic individuals that a given susceptible individual may encounter is , and the total number of susceptible individuals exposed to infectious symptomatic cases is . Likewise, that for asymptomatic cases, the rate of symptomatic infections is . These terms drive the creation of new infections in the population. The force of the symptomatic group is the coefficient of , or . The number of the susceptible group that an individual can infect over their entire period of infectiousness is the reproduction number = , and similarly for the asymptomatic infectious group. These numbers primarily drive the rate of growth of the infection in the population, which early in the expansion is measured by the doubling time.