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

Daniel E Platt; Laxmi E Parida; Pierre Zalloua

Compartmental models count individuals at different stages of progression of a disease, where each stage of progression is marked by an event that has a well-defined rate. For example, from time of infection to the time the person can transmit disease has a time distribution, that, for enough people in the compartment, will tend to center on an average by the central limit theorem for large enough samples drawn from any given distribution. There is evidence that COVID-19 presents symptomatic cases and asymptomatic cases, with asymptomatic cases [10] [11] [12] less likely to be identified and isolated [13] [14] [15] [16] [17] . There is an incubation period after infection that lasts until the incubating individuals become infectious. There has been some early estimates based on confirmed cases 13, 18 with more evidence of pre-symptomatic transmission being noted 19, 20 yielding faster incubation. Incubation partly accounts for the observed lag when social distancing or other viral spread prevention policies are imposed. For the most part, infections appear to be transmittable prior to overt symptoms, allowing for a pre-symptomatic period that may convert to symptomatic. At the same time, some of those asymptomatic people remain asymptomatic until they are non-contagious 11 . Patients may still be infectious for several days after symptomatic recovery. Symptomatic patients likely to be hospitalized are hospitalized more quickly than non-hospitalized patients recover. Hospitalized patients in ICU or required immediate ventilation tend to experience a longer time to recovery than nonhospitalized patients. Those that stay on the ventilator for long periods tend to have a high mortality rate, and may stay on the ventilator for many weeks prior to dying. 8 A compartmental model that captures the conditions status and durations count susceptible population members , incubating , infectious asymptomatic , infectious symptomatic , infectious people who will be hospitalized , those hospitalized who recover , and hospitalized leading to mortality . Recoveries are , and mortalities are . The time from exposed to infectious is , where is partitioned into contributions to asymptomatic infectious , symptomatic infectious , and infectious that will be hospitalized , so that = + + . Total removal time among asymptotic infectious is , with a fraction going to infectious symptomatic. Infectious symptomatic removal time is . The period prior to hospitalization is ( + ) . The rate that the proportion that recovers is , and that which dies is . The model equations, reflecting an underlying Markov chain, expressing these connections and rates are: Table 1 .