Modeling Epidemics: A Primer and Numerus Software Implementation

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

We note that solutions to this discrete system will differ from solutions to the continuous system, even for constant Λ(t), because τ (t) does not remain constant over the interval (t, t + 1] in the continuous model ( Figure 4) . However, there is no a priori reason to favor a continuous over a discrete time formulation because the data represent averages of discrete events (that is, transitions of individuals from one disease class to another, or the occurrence of deaths) rather than continuous, smooth flows. In fact, stochastic approaches are needed to capture the full richness of epidemiological dynamics [8, 9, 17] and, as discussed below, it is far easier to make discrete-time models stochastic than continuoustime models.