A mathematician would say that the model comprises the equation or system of equations that describe the thing being modeled. Whether or not a usable computational model can be constructed is another matter entirely. This is, in fact, where the IPCC's models and other complex GCM "fall down." Lack of computational capacity forces them to be run using coarse spatial scales, resulting in output that would be inaccurate or erroneous even if the models were theoretically complete (which they are not). For more on this problem see "Extinction, Climate Change & Modeling Mayhem."