system
Given the following post, respond as if you're commenting on Reddit:
human
[Children of Men] What happens next?

Would the Human Project try to deduce what made Kee fertile and be able to distribute that to enough people to save humanity? Best case scenario, how bad of a genetic bottleneck is humanity about to go through?
gpt
Movie:
The world's problems aren't solved overnight. Kee will be jealously guarded by the Human Project, poked, prodded, and put through all sorts of tests, along with her child. If from her they can come up with the miracle that will save mankind, that will allow women to have children again, there will still be a number of issues to overcome.

From what we know, the rest of the world has gone entirely to shit, so England is the logical place to try to spread the cure, there is still good infrastructure and medical services, both of which will be necessary to distribute it effectively. Unfortunately, these services are held together by an oppressive government who, once they know there is a cure, will likely do whatever they can to take control of it and maintain their hold on power. From there they can save Britain, and then use the cure as leverage against the rest of the world to set up an international system that is heavily in their favour. 

Assuming that the entire population of Britain can receive the cure in a relatively short amount of time there will be an almost immediate population boom. People who lived through the depression of knowing they were the last generation of humanity will joyfully breed like rabbits once they find out the world is saved. Luckily, it being only 18 years since the last human was born, there will still be a great number of professionals with relevant experience. There will be enough midwives, pediatric doctors, elementary school teachers, etc. who survived to train the next generation to ensure that the baby boom will be effectively looked after.

Once children start being born again after a few years things will return to normality, for the first decade or so there will be a massive population imbalance towards the elderly and middle-aged which will turn into a massive imbalance towards teens and twenty-somethings once that generation starts to die of old age. This cycle will repeat several times with decreasing severity as each successive generation reaches the typical age of reproduction.

The children of the first generation after general infertility will also likely be spoiled brats. Children will be guarded jealously, protected, and likely coddled by parents who thought they would live to see the end of their race.  Children will be treated as something precious, and its likely that the safety of children will be considered the top priority of society. It's likely that this generation will grow up with a massive sense of entitlement.

Book:
Theo, using his relationship as the previous Warden of England's cousin and being the self-declared protector of Miriam and her child, will take over the role of Warden of England. Using his position of power he ensures that the cure, when found, is spread to all of Britain, and then the rest of world as well as he can. 

There is a problem with raising the next generation however, the last child was born almost 30 years ago, most of those who would be best able to raise a new generation are seniors at this point, and may not live to see the new generation reach their teens. The Omega generation, the last generation born before infertility, would be young enough, but with their sense of entitlement and superiority, their casual violence and general disregard for their seniors and the rest of humanity in general, would make unreliable shepherds for the next generation. Unfortunately, once the older generations die out, they will be the only ones left to take care of the children of the next. It is possible that some knowledge may be passed on, but without the tutelage of the rapidly aging previous generations it is likely that decades, if not centuries of knowledge will be lost. Humanity will enter a new dark age, but in time, we will recover.