Re: damn carthage...
They'll continue for as long as the Carthaginians hold Sicily. Get a spy to Sicily so you can spot incoming fleets. Hold them off until the invasion forces consist mainly of Liby-Phoenician spears, then prepare an invasion force of your own for a Sicilian expedition. Leave a minimal force (mainly auxiliaries) in the north to fend off further invasions, then ship the bulk of your army to Sicily to take the island from the Carthaginians. Once the whole of Sicily has been taken, the Carthaginian invasions of Italy will stop.
Afterwards, take all the western Mediterranean islands you can, before sending a diplomat to Africa to ask for peace. The Carthaginians will usually accept, and once they've done so, they'll usually keep the peace for the rest of the game, meaning security and prosperous trade on the western side of Italy while you concentrate on the east.