Modeling epidemics: A primer and Numerus Model Builder implementation.

Area of Science:

• Epidemiology
• Mathematical Modeling
• Computational Science

Background:

• Compartmental models, particularly Susceptible-Infectious-Recovered (SIR) formulations, are foundational in epidemiological modeling.
• SIR models exist in various forms: continuous, discrete, deterministic, stochastic, and spatially homogeneous/heterogeneous (networked).

Purpose of the Study:

• To review diverse SIR dynamical systems model formulations.
• To demonstrate the rapid construction of these models using Numerus Model Builder (NMB).
• To illustrate extending SIR models to metapopulation networks via NMB tools.

Main Methods:

• Review of continuous and discrete deterministic SIR model formulations.
• Review of discrete stochastic SIR model formulations.
• Demonstration of model construction and metapopulation extension using NMB's graphical interface and network/mapping tools.

Main Results:

• Comprehensive overview of SIR model variations and their characteristics.
• Efficient and rapid model construction is achievable with NMB.
• NMB facilitates straightforward extension of SIR models to complex metapopulation network structures.

Conclusions:

• NMB provides a powerful, user-friendly platform for developing and extending epidemiological SIR models.
• The graphical approach of NMB simplifies the implementation of complex model dynamics and network structures.
• This work highlights NMB's utility for researchers in epidemiology and computational modeling.