Modeling Epidemics: A Primer and Numerus Software Implementation

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

Hethcote [10] provided a comprehensive review of the fundamental deterministic dynamics of SEIR models and their elaboration to include an M class (that is, individuals born with maternally provided immunity that wears off over time), and elementary characterizations of birth and death process. His results have been considerably extended to elaborated SEIR models that include more complex characterizations of births and of deaths, and some age-structure -with a strong focus in the mathematics literature on the existence and stability of outbreak and endemic equilibria [11] . Analyses of stochastic SEIR models and elaborations remain more challenging, though some analytical results do exist. Most stochastic analyses, however, are computationally intensive and the results numerical rather than analytical. In addition, unlike deterministic SEIR models which are readily fitted to data, it remains a challenge to fit stochastic models to data, with new approaches involving concepts well beyond first courses in calculus or linear algebra.