In the movie Children of Men, the focus is on a former activist (Theo) as he escorts and protects a pregnant woman (Kee) across the U.S, a country at this time barren and deep into chaos as infertility has dimished the human population for 18 years. The U.K seems to be the only functioning nation where most go to escape the violence, thus this was their goal. While they do reach the base, the fighting comes to them as they prepare for embarking the Tomorrow, and Theo is shot. Finally, Kee gives birth to a baby girl, who she names Dylan. This shows light and hope amidst a storm of chaos and war.
So what might seem similar here to the Hunger Games? Dylan seems to be the Mockingjay here, where she is the symbol of hope and retribution, even moreso, the symbol of the rebirth of what seems to be the remnants of planet Earth. While Dylan is only born once, Katniss goes through numerous 'rebirths' to become the symbol of the rebellion that she became by the end of book 3. The fact that both characters exist creates beacons of hope in their respective stories, where Dylan signifies the end of Human sterility in the otherwise barren world Earth became, and Katniss signifies the end of Human oppression in the ravaged, post-apocalyptic world that Panem became.