Modeling Epidemics: A Primer and Numerus Software Implementation

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

where k ∈ [0, 1] switches the emphasis from the population size factor to the prevalence factor as k increases in value from 0 to 1. The inputs h X i (t) and per-capita flow rate outputs q X i (X=S, E, I and V) for the focal i th subpopulation, can either be 0, constants, or generated using probability distributions in stochastic versions of the model. The inputs will, of course, depend on the density or number of individuals available in the environment surrounding the focal subpopulation i, with population structure taken into account using network or nearest neighbor concepts. In the context of discrete deterministic or stochastic models, we need to account for the per-capita flow rate outputs q X in our competing rates formulations to obtain the extended probability for the case of rates assumed to be constant over each interval of time (though the rates themselves can vary from one time interval to the next). In this case, we augment the proportions/probabilities in Equation 10 to define the following terms for All rights reserved. No reuse allowed without permission.