When Hannibal was leading his campaign against the Romans, how was it that the news of Romans launching a campaign near his home in North Africa traveled quickly enough back to him such that he had enough time to go back and engage them? What form of communication/transportation was used in that time period?
From 216 onwards, once significant parts of southern Italy joined Hannibal's side, Hannibal was in regular contact with Carthage. For much of the war there were Carthaginian forces in Sicily (between southern Italy and Carthage) and Roman dominance at sea wasn't yet to point where the could stop Carthaginian ships from going between Italy and Carthage. Hannibal even requested and received reinforcements (several thousand men) from Carthage. Later on the war movement by ship became more and more dangerous for the Carthaginians as Rome gained the upper hand in the war and drove the Carthaginians from Sicily.
If Rome was in control of the sea and land between Hannibal and Carthage, how then did he get back to North Africa safely and in time? The answer is quite simple: the Romans let him go!
Roman forces, led by Scipio, had landed in North Africa in 204 and defeated Carthaginian forces in 204 and 203. Hannibal had already been called back by Carthage's leaders, but he didn't return in time. After the defeats, the Carthaginians entered peace talks with Scipio; they agreed on a treaty which included the withdrawal of Carthaginian forces from Italy. This allowed Hannibal to return to North Africa without any problems.
With Hannibal and his army back in North Africa, the Carthaginians regained their will to fight. A couple of incidents involving the looting of a Roman supply ship and the mistreatment of Roman envoys led to a resumption of the war. Hannibal fought Scipio and the Battle of Zama in 202 and lost. Mostly defenseless, Carthage now had no option but to accept new - harsher - peace terms.
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