Consider a scale-free network that represents the collaboration structure among software developers. Empirical evidence indicates that this network exhibits a power-law degree distribution with an exponent in the range 3 < \( \gamma \) < 4. An SIS epidemic process unfolds on this network. Which of the following statements best characterizes the epidemic dynamics in this scenario?
A. There is no epidemic threshold, and any arbitrarily small spreading rate \( \lambda \) results in a non-zero endemic prevalence.
B. There exists a finite epidemic threshold \( \lambda_c \) > 0; for \( \lambda > \lambda_c \), the prevalence increases with \( \lambda \) following a nonlinear power-law behavior, characterized by a critical exponent different from 1.
C. The prevalence increases linearly with \( \lambda \) - \( \lambda_c \) near the threshold, as observed in homogeneous mixing models.
D. At \( \lambda = \lambda_c \), the system undergoes a discontinuous transition from zero prevalence to a finite value, indicating a first-order phase transition.
E. None of the above.
Original idea by Jonas Henrique Ribeiro Paula
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