Modeling Epidemics: A Primer and Numerus Software Implementation

Wayne M. Getz; Richard Salter; Oliver Muellerklein; Hyun S. Yoon; Krti Tallam

Though the fits are similar-both, for example predict an initially β around 1.5 that drops to half that level in just over two weeks after the first cases have been detected-the LSE fit predicts an 14% smaller initial population at risk than the MLE fit. Thus the errors associated with this estimation can be quite large, and require a Bayesian type Markov Chain Monte Carlo (MCMC) approach to estimate them. Further, as is evident from our plots in Figure 8B , if we use the first T weeks of data, T = 10, 20, 30, and 40,to fit the model, we see that fitting the first 10 weeks (red curve) greatly overestimates the final size of the epidemic, while fitting the first 20 weeks somewhat underestimates the final number of cases. Before leaving this example, we note that in several runs of the optimization algorithm, different starting conditions converged to different solutions, thereby indicating that some of these solutions are local rather than global minimum. When this happened, we selected the solution that gave the lowest log-likelihood value, but our searches were not sufficiently exhaustive for us to be sure that we had found the global minimum for each case.