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If $I$ is the infected population and $C$ is the cure capacity per day, for the protagonist to save the world, $C$ must eventually exceed the rate of new infections. Given that a zombie horde can number in the thousands and spread infection rapidly, the protagonist faces a mathematical impossibility. He cannot physically "out-heal" the contagion on a global scale.
If $I$ is the infected population and $C$ is the cure capacity per day, for the protagonist to save the world, $C$ must eventually exceed the rate of new infections. Given that a zombie horde can number in the thousands and spread infection rapidly, the protagonist faces a mathematical impossibility. He cannot physically "out-heal" the contagion on a global scale.
