EoN.Attack_rate_cts_time¶
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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
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.