Modeling Epidemics: A Primer and Numerus Software Implementation

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

Here, for purposes of illustration, we fit our deterministic SEIV model to the Sierra Leone Ebola weekly incidence data [61] using both LSE and MLE approaches (Figure 8 : cf. fits obtained in [47] ). When fitting such data the appropriate initial conditions are generally uncertain because detection of the putative index case does not generally pin down the start of the epidemic: the actual index case may often go undetected and the number of individuals in class E at the time of the first case is also unknown. Thus, as part of the fitting procedure, we allow the initial values E(0), I(0) in the model to be fitted to the data. To keep the dimensions of the fitting problem down, however, we set E(0) = I(0) = Z and the search for the best fitting value of Z. Another imponderable is the actual number of individuals N (0) at risk at the start of the epidemic. Thus we also treat N (0) = N 0 to be an optimization parameter, though we set V (0) = 0 under the assumption that if some individuals in the population were immune to Ebola at the start of the epidemic, this would be reflected in Figure 4) has been fitted to Ebola data from the Sierra Leone 2014 outbreak in which more than 10,000 cases occurred during the course of an approximately one-year period [61] . A. The blue and red curves are the best fit LSE (cf. Equation27 and MLE (cf. Equation 28 obtained with the optimal parameter sets given in the text. B. The black dotted line is the MLE fit, as in Panel A, with the red, orange, purple and blue plots, simulations obtained after obtaining the best MLE fits to the first 10, 20, 30 and 40 weeks of incidence respectively. See Video 9 at the supporting website for more information on how to set up and run optimizations on this model using Numerus Model Builder. a lower-valued estimate of N 0 . Thus N 0 should be interpreted as the "initial population at risk" rather than actual popultion size. Also, in preliminary runs of our optimization algorithm (i.e. when fixing diffent combinations of parameters and solving reduced parameter set problems), the difference between optimal values for σ and γ under variety of settings always lead to opti-All rights reserved. No reuse allowed without permission.