Modeling Epidemics: A Primer and Numerus Software Implementation

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

Underpinning all dynamical systems models of epidemiological outbreaks and endemics disease are formulations based on the concept of an SEIR progression (Figure 1 ), whereby susceptible individuals in disease class S enter disease class E on exposure to a pathogen (i.e., infected but not yet infectious themselves). Individuals in class E then transfer, after a period of latency, into the class of infectious individuals, I, only to trans-fer on recovery or death to a removed class R. The recovered individuals may have some temporary, though possibly long term, immunity (V) and death (D) can arise from both natural and disease-induced causes (i.e., R=V+D). Variations and elaboration of the the SEIR process may include birth and death processes, other demographic class such as age [2] and sex [3] , spatial structure [4, 5] , and the genetic structure of hosts and pathogens [6, 7] . Further, stochastic formulations of SEIR models [8, 9] are increasingly being used to explore the inherent and very important stochastic aspects of epidemics including, probabilities of fadeouts versus breakouts in the early stages of epidemics, and logistical planning necessary for managing epidemics of uncertain ultimate size.