Epidemiological models are dominated by compartmental models, of which SIR formulations are the most commonly used. These formulations can be continuous or discrete (in either the state-variable values or time), deterministic or stochastic, or spatially homogeneous or heterogeneous, the latter often embracing a network formulation. Here we review the continuous and discrete deterministic and discrete stochastic formulations of the SIR dynamical systems models, and we outline how they can be easily and rapidly constructed using Numerus Model Builder, a graphically-driven coding platform. We also demonstrate how to extend these models to a metapopulation setting using NMB network and mapping tools.

Epidemiological models are dominated by SEIR (Susceptible, Exposed, Infected and Removed) dynamical systems formulations and their elaborations. These formulations can be continuous or discrete, deterministic or stochastic, or spatially homogeneous or heterogeneous, the latter often embracing a network formulation. Here we review the continuous and discrete deterministic and discrete stochastic formulations of the SEIR dynamical systems models, and we outline how they can be easily and rapidly constructed using the Numerus Model Builder, a graphically-driven coding platform. We also demonstrate how to extend these models to a metapopulation setting using both the Numerus Model Builder network and geographical mapping tools.