The art of modeling

John M. Drake

What are models for?


Discussion: Why make a model?

What are models for?


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

Some principles


  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

Some data

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Questions

  1. What is the etiological agent?
  2. Is it novel?
  3. What is the spectrum of presentation?
  4. How should cases be treated?
  5. Is a vaccine available?

Where does modeling fit it?

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

Some population level questions


  • 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?

Some questions about control


  • 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?

Emerging pathogens vs endemic diseases


Models are appropriate for both emerging and endemic diseases, but depending on the epidemiology may emphasize different aspects of transmission and control.


Emerging pathogens arise in a wholly susceptible population and may exhibit transient trajectories (epidemics) that are far from equilibrium

Endemic pathogens exhibit quasi-stationary behavior

What is a model?


  • 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

Different kinds of models


Developments in recent years have blurred these categories significantly

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

The art of modeling: Idealization