# EoN.Attack_rate_cts_time¶

EoN.Attack_rate_cts_time(Pk, tau, gamma, number_its=100, rho=None, Sk0=None, phiS0=None, phiR0=0)[source]

Encodes system (6.7) of Kiss, Miller, & Simon. Please cite the book if using this algorithm.

This system predicts the fraction of nodes infected if an epidemic occurs in a Configuration Model network assuming a continuous-time Markovian SIR disease.

This gives the limit of the attack rate of epidemics as the initial fraction infected approaches 0.

If we look for the limit of a nonzero initial fraction infected, we introduce rho or Sk0

Pk dict
the probability a randomly selected node has degree k.
tau positive float
per-edge transmission rate.
gamma number
per-node recovery rate
number_its int
The solution is found iteratively, so this determines the number of iterations.
rho number, optional
The initial proportion infected (defaults to None). If None, then result is limit of rho->0.
Sk0 dict (default None)
only one of rho and Sk0 can be defined. The other (or both) should remain None. rho gives the fraction of nodes randomly infected. Sk0 is a dict such that Sk0[k] is the probability that a degree k node is susceptible at start.
AR float
the predicted fraction infected.