The art of modeling

Discussion: Why make a model?

• Estimation
• Inference
• Prediction
• Scenario analysis
• Coherence (“sanity check”)
• Synthesis

1. The model is only as good as the data it's based on

2. A model is just an idea

Exercise: Critique these perspectives

Note: Models can't make up for what we lack in empirical information

Infectious disease management requires a multi-disciplinary approach

• Medicine
• Genetics/Genomics
• Microbiology
• Immunology
• Vaccines & Drugs

Although each of these approaches are important for understanding individual response and clinical care they don't address important questions at the population level

• Will this disease invade the population or go extinct?
• How fast will it grow?
• When will the epidemic peak?
• When will it disappear?
• Is it evolving? If so, why and how fast?

• How to prevent spatial spread?
• How to prevent reintroduction?
• When is it best to implement interventions?
• How drastic of an intervention is required for containment?
• Should interventions be general or targeted?
• What interventions will be most effective?

• A model is an abstract representation of a system
• A model is the mathematical or computational description of an idea
• A model is described in terms of its state and processes that result in a change of state
• In compartmental models, the primary focus of this course, these are often represented by two kinds of variables, referred to as the state variables and the parameters

Developments in recent years have blurred these categories significantly

• Statistical (including AI) vs mechanistic
• Deterministic vs stochastic
• Compartmental models
• Agent-based models
• Network models

Choice of model depends on

1. The purpose for which the model is constructed (estimation, inference, prediction…)
2. The information (or data) available to inform the model

• Precision/Accuracy

Model complexity (number of state variables, nonlinearity)

Ability to account for observations

• Intelligibility

Intelligible to human consumers/decision-makers

• Flexibility

Adaptability to new scenarios

Brett T, et al. (2020) Detecting critical slowing down in high-dimensional epidemiological systems. PLoS Comput Biol 16(3): e1007679.

Brett T, et al. (2020) Detecting critical slowing down in high-dimensional epidemiological systems. PLoS Comput Biol 16(3): e1007679.

Brett T, et al. (2020) Detecting critical slowing down in high-dimensional epidemiological systems. PLoS Comput Biol 16(3): e1007679.

• Express concept mathematically (equations, rates of change, etc.)
• Solve analytically (the general solution) or numerically (specific solutions) – Note: only the simplest models are analytically tractable
• Ready made software (e.g. ModelMaker, R packages, Berkeley Madonna)
• “Big” simulators (GLEAM, MOBS, etc.)
• Note on terminology: simulation vs solution