Purposes of
Mathematical Modeling of Populations

• The model formulation process clarifies assumptions, variables, and parameters.
• The behavior of precise mathematical models can be analyzed using mathematical methods and computer simulations.
• Modeling provides concepts.
• Modeling is an experimental tool for testing theories and assessing quantitive conjectures.
• Models with appropriate complexity can be constructed to answer specific questions.
• Modeling can be used to estimate parameters by fitting data.
• Models provide structures for coalescing and cross-checking diverse pieces of information.
• Models can be used in comparing populations of different types at different times.
• Models can be used to evaluate, compare, and optimize various detection, prevention, and control programs.
• Models can be used to assess the sensitivity of results to changes in parameter values.
• Modeling can suggest information which needs to be collected.
• Models can be used to identify trends and make general forecasts.

• Models are not reality; they are an extreme simplification of reality.
• Deterministic models do not reflect the role of chance and do not provide confidence intervals on results.
• Models that incorporate randomness are harder to analyze than the corresponding deterministic models.

  adapted from Herbert W. Hethcote