Let me tell you how populations density goes in reverse.. Big Wars, and Big disease followed by Big famine. At least that is the past history.
Have you read
Inferno by Dan Brown? I can't say much about the population control-related plot without ruining it for someone who might read it.
Big War seems less likely to me than in past times, but who knows?
World War II casualties - Wikipedia, the free encyclopedia
World War II was the deadliest military conflict in history. Over 60 million people were killed, which was over 2.5% of the world population.
2% of 7 billion people is 140 million.
3% of 7 billion people is 210 million.
Those would be the losses required to be equivalent to the magnitude in WWII. It didn't take very long to recover the (total) population following WWII.
These are the 2011 global estimates:
131.4 million births per year 55.3 million people die each year
That is a net growth of 76.1 million per year and accelerating. It would take less than three years to recover a 3% population loss at those rates. Although, a higher average global age would tend to slow that rate of recovery since a larger portion of the population would be beyond their child-bearing ages.
Big viral Disease is possible certainly. It's questionable if governments would act quickly and aggressively enough to contain a highly communicable viral disease. Would regional quarantines be erected early enough to be effective? How would that be enforced? Would we shoot down a civilian airliner coming from an infected region?
Big Famine on a global scale. Has that happened in the past, or could it happen globally now? A big volcanic or space object (comet, meteor, asteroid) event could certainly put a dent in global food supplies and reserves for a period of years.