Discrete Epidemic Models with Arbitrary Stage Distributions and Applications to Disease Control

A deterministic discrete-time epidemic model is introduced in this poster. We expand on models studied previously through the inclusion of arbitrary exposed and infectious period distributions. Results that allow us to measure quantitatively the role of classical and general distributions in the model predictions on disease dynamics are presented. The geometric distribution is used to set up the baseline or null epidemiological model used to test the relevance of realistic stage-period distribution on the dynamics of single epidemic outbreaks. A final size relationship is computed and our derivations help reveal the explicit dependance of the control reproduction number R_c on the mean values of the stage distributions, the mean sojourn times, and the quarantine-adjusted probability. Model results and simulations highlight the inconsistencies in forecasting that emerge from the use of specific parametric distributions.