# 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}
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
PE float
Calculated Epidemic probability (assuming configuration model)