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