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

Daniel E Platt; Laxmi E Parida; Pierre Zalloua

One of the major goals of epidemic modeling is to predict mortality and resource load on community medical facilities: how many beds, how many ventilators, how much pharmaceuticals, among other resources will be needed to get through the epidemic. Early epidemic growth for this system is dominated by the largest eigenvalue of 9 coefficients governing the rate-limiting variables. This eigenvalue determines the doubling time of the growth, and imposes one constraint on those coefficients; the eigenvectors impose three more constraints on the system, leaving five coefficients undetermined. Essentially, all of the ratelimiting relevant epidemic variables grow at the same rate maintaining fixed ratios. However, as they near peak, the variable trajectories become more differentiated, with lagging or leading peaks emerging as the impact of filters through the system of equations. However, at peak, it is already too late to allow time to acquire and deploy needed resources to hospitals and clinics. By itself, the trajectory of these models in pre-peak growth offer little hint as to final needs. Further, there are a number of combinations of parameters that would yield the same leading eigenvector and eigenvalue.