Most of the models so far proposed, however, solve the problem of a single vehicle independently of the entire traffic flow, and so are not completely coupled. An example is a PDE-ODE model that used a partial differential equation to model the flow of traffic while using an ordinary differential equation to determine the position of a single vehicle. Since both could be solved independently, the system did not take into account the influence of the single car on the entire traffic flow.
The paper by Lattanzio et al provides a fully coupled, multi-scale model in which the microscopic position of a single car is taken together with the macroscopic car density on the road.
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Difference between Integration and Differentiation