Paper Information

Science involves perceiving patterns (events that are repeated) in observations, hypothesizing causal explanations (underlying processes), and testing them. Mathematical models either describe or provide explanations for patterns. The equations of descriptive models have convenient mathematical properties while those of mechanistic ones correspond to processes. The parameters of descriptive models are fit to observations by choosing values that minimize discrepant predictions. Because mechanistic models are hypotheses about the processes underlying patterns, their parameters should not be fit, but rather, should be based insofar as possible on first principles or estimated independently. The precision of mathematics facilitates comparing the predictions of mechanistic models to the patterns that they purport to explain and, until concordant, identifying and remedying the cause(s) of disparities. The findings and conclusions in this report are those of the authors and do not necessarily represent official positions of the Centers for Disease Control and Prevention or National Science Foundation.