Ellie is immune because the Cordyceps fungus was already present in her system from birth. This early presence of Cordyceps acts like a "chemical messenger" that makes new Cordyceps infections think she is already infected, preventing the fungus from taking hold and making her immune to its effects. This unique condition happened because her mother was bitten by an infected just before Ellie was born, passing the fungus to Ellie during birth, but not enough to actually infect her. The Cordyceps in her system essentially protect her by tricking new infections.
