Systems and methods for controlling temperature and total hydrocarbon slip in an exhaust system are provided. Control systems can comprise an oxidation catalyst, a particulate filter, a fuel injector, and a processor for controlling a fuel injection based on an oxidation catalyst model. Example system includes a virtual sensor comprising a controller for calculating and providing the total hydrocarbon slip to subsystems for after-treatment management based on modeling the oxidation catalyst. Example methods for controlling the temperature and the total hydrocarbon slip in an exhaust system include the steps of providing an oxidation catalyst model, monitoring a condition of the exhaust system, calculating a hydrocarbon fuel injection flow rate and controlling a fuel injection. The example methods further include the steps of determining an error in the oxidation catalyst model based on the monitored condition and changing the oxidation catalyst model to reduce the error.