The Secretary of Defense under John F. Kennedy was Robert McNamara. Those two men were the ones most in charge of the Cuban Missile Crisis in 1962 when the world came within one hour of a real Doomsday, and therefore McNamara’s opinion on this subject is to be observed carefully. He said that if an atomic war were to begin, he saw no way of stopping it from running its full course. He was referring primarily to a war between the USA and the USSR, but he implied that it also applied to smaller, what was then termed brush-fire, wars. It is impossible to know what would happen today, but it is easy to postulate an infinity of possible sparks that might ignite an absolute conflagration.
The most reasonable, and rational of reasons for a major war is when there is a major food shortfall which results in widespread famine. In that desperate case any starving nations would have little to lose, and potentially much to gain by robbing another country of its food supplies. That of course would mean the victim nation’s people would starve. Those potential victim people would of course realize that, and fight back with absolute ferocity, and use their own A-bombs if they possessed them. Or if they did not possess A-bombs, they would attempt to drag other atomic bomb possessing powers into the battle to aid them.
Local famine is presently avoided because of the very efficient transportation systems moving bulk quantities of material such as food to other parts of the world, and so when a major food shortfall hits one part of the world it can be adjusted to by shipping in large quantities of food from other places where it is more abundant. With the total population of the world continuing to explode there will come a time when the world’s people’s need for food will exceed the supply. Assuming a stable world to exist when this major food shortfall finally happens the graphs resulting from that major war would look like this:
Note that in this scenario the quantity of food tops out and begins to decline, and the population only flattens out. This occurs because even if there were no new babies born the existing population has a 40+ year life expectancy, and would continue to live as long as there is food available to keep them alive. However, as the reserves are consumed there will come a time of worldwide desperation. While this crisis develops there will be great efforts to convert marginally producing farms into quickly producing ones. That will work, but only for a short time, before they become depleted, and a continuing shortfall will move into an absolute crisis mode. A major atomic war triggered by world famine would then have a chart with the general appearance of the one above.
A different scenario might occur with a limited atomic war or an accidental one which was triggered when there was no absolute shortfall of some critical basic material such as food. This might come about because of some long standing political or ideological antipathy. The reasons may seem obscure even irrational to outsiders, but to the the parties involved they tend to be very clearly defined, by various absolute convictions. A war of this type might remain localized, because the reasons for the battles are irrelevant to those outside of the combatant groups. It is just as likely that others outside of the conflict would be drawn into the conflagration such as happened in WW I where over the course of several weeks all Europe became twisted into unrecognizable political knots of deadly interrelationships. The same will likely happen when this type of limited atomic war erupts. However, in this postulated case the results will happen in hours rather than weeks, and months, and the results will immediately be life threatening for everyone on the planet.
Even a local limited modern atomic war will have instant, and sustained consequences for everyone. The instantaneous deaths of many of the combatants, and their civilian populations will be horrible, and quick, but then there will be several months of deaths from radioactive fallout, and then more deaths from disease. These disasters will be relatively localized to zones of death which are well defined within a week or two; except for diseases which may be militarized, and totally uncontrollable, and with unknowable limits. Most of these secondary deaths could be prevented if the infrastructure wasn’t destroyed or people knew what they had to do to save themselves, but for these first few critical weeks there will be chaos, and everyone will tend to keep doing either nothing, or continue doing whatever their life task has been before the Doomsday events occurred, and neither of those will work very well in this catastrophic situation.
This scenario assumes the superpowers do not get involved in the attacks, and that is possible, but unlikely, and the war will be a limited one only if there has been time to prepare for the non-war with Doomsday event avoiding agreements. The superpowers would have to have pre-agreed not to do anything militarily, when the lesser powers decided to go nuclear. But, who can trust anyone to do what they said they were going to do, when these A-bombs start falling.
The after effects of a local limited war will drag on for years with its cumulative effects which are caused by the breakdown of the world order. This will happen because shipping, and other forms of commerce will suddenly stop because moving valuable things out of country, or even within it will be risky when the laws, and social order are unknown. If there is no certain way to be paid for a product then that product will not be shipped, nor will it be produced, and then workers will neither be needed nor paid. Soon poor people, and even previously rich ones may find that they have nothing of value which can be traded for the most common of current commodities—food. This food shortage will happen, when food ceases to be shipped around the world, and there will soon be local famines which spread to surrounding areas. Where fuel oil and energy are not available for the farm machinery it will not be operated, and food will not be created, and even that which is created will kept locally, and not be shipped. Thus it is possible that with even a limited war, especially one involving oil producing countries, there will be widespread famine, and the population of the world will plummet.
The chart above shows a vertical drop in all of the plot lines on the day of the war (except for pollution which rockets upward, and off the chart), but food supply continues to drop for a long time afterwards, and it is soon followed by the population curve. The food curve, and the population curve do not stabilize, and start to rise again until available resources especially oil become reliably available. It takes a while to get these industries going again because of the social chaos, and questionable markets. Eventually, after, who knows, ten years the social order will be restored and people can approach again the abundance, and tranquility we now take for granted.