EoN.Epi_Prob_cts_time¶
-
EoN.
Epi_Prob_cts_time
(Pk, tau, gamma, umin=0, umax=10, ucount=1001, number_its=100)[source]¶ Encodes System (6.3) of Kiss, Miller, & Simon. Please cite the book if using this algorithm.
The equations are rescaled by setting $u=gamma T$. Then it becomes
P = 1- int_0^infty psi(alpha(u/gamma)) e^{-u} du alpha_d(u/gamma) = 1- p(u/gamma)
p(u/gamma) int_0^infty
(psiPrime(alpha(hat{u}/gamma))/<K>) e^{-u}du
where p(u/gamma) = 1 - e^{-tau u/gamma}
- Define
- hat{p}(u) = p(u/gamma), and hat{alpha}(u) = alpha(u/gamma)
and then drop hats to get
P = 1-int_0^infty psi(alpha(u)) e^{-u} du alpha(u) = 1-p(u) + p(u)
- int_0^infty
- (psiPrime(alpha(u))/<K>)e^{-u} du
- with initial guess
- alpha_1(u) = e^{-tau u/gamma}
- and
- p(u) = 1-e^{-tau u/gamma}
Arguments: - Pk dict
- Pk[k] is probability a node has degree k.
- tau float
- transmission rate
- gamma float
- recovery rate
umin minimal value of gamma T used in calculation umax maximum value of gamma T used in calculation ucount number of points taken for integral.
So this integrates from umin to umax using simple Riemann sum.- number_its int
- number of iterations before assumed converged. default value is 100
Returns: - PE float
- Calculated Epidemic probability (assuming configuration model)