EoN.Attack_rate_cts_time

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

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

Arguments:

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.

Returns:

AR float

the predicted fraction infected.