There's this Early Stopping function that Keras supply which you simply define.
EarlyStopping(patience=self.patience, verbose=self.verbose, monitor=self.monitor)
Let's say that the epochs parameter equals to 80, like you said before. When you use the EarlyStopping function the number of epochs becomes the maximum number of epochs.
You can define the EarlyStopping function to monitor the validation loss, for example, when ever this loss does not improve no more it'll give it a few last chances (the number you put in the patience parameter) and if after those last chances the monitored value didn't improve the training process will stop.
The best practice, in my opinion, is to use both EarlyStopping and ModelCheckpoint, which is another callback function supplied in Keras' API that simply saves your last best model (you decide what best means, best loss or other value that you test your results with).
This is the Keras solution for the problem your trying to deal with. In addition there is a lot of online material that you can read about how to deal with overfit.