• Only sufficiently frequent attacks, with increasing force, will result in eradication, assuming the available resources can be mustered in time.
• The authors of an article called “When Zombies Attack!: Mathematical Modeling of an Outbreak of Zombie Infection” • Discussing how to survive a zombie attack. The authors also note that the attack has a limited timeframe. In a city of 500,000, you have about three hours to prevent the level of zombies from topping the level of humans. So basically, you need to be Simon Pegg to survive. • source

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