EoN.SIS_compact_pairwise

EoN.SIS_compact_pairwise(Sk0, Ik0, SI0, SS0, II0, tau, gamma, tmin=0, tmax=100, tcount=1001, return_full_data=False)

Encodes system (5.18) of Kiss, Miller, & Simon. Please cite the book if using this algorithm.

[dot{S}_k] = gamma[I_k] - tau k [S_k] [SI]/[SX]

[dot{I}_k] = tau * k *[S_k] [SI]/SX - gamma [I_k] = -[dot{S}_k]

[dot{SI}] = gamma([II]-[SI]) + tau([SS]-[SI])[SI]Q - tau[SI]

[dot{SS}] = 2 gamma[SI] - 2 tau [SS] [SI] Q

[dot{II}] = 2 tau[SI] = 2 gamma[II] + 2 tau[SI]^2Q

[SX] = sum_k k [S_k]

Q = (1/[SX]^2) sum_k (k-1)k[S_k]

Conserved quantities:  

[Sk]+[Ik]

SS + II + 2SI

Arguments:

Sk0 numpy array

number susceptible for each k

Ik0 numpy array

number infected for each k

SI0 number

number of SI edges

SS0 number

number of SS edges

II0 number

number of II edges

tau positive float

transmission rate

gamma number

recovery rate

tmin number (default 0)

minimum report time

tmax number (default 100)

maximum report time

tcount integer (default 1001)

number of reports

return_full_data boolean (default False)

if True, return times, S, I, Sk, Ik, SI, SS, II if False, return times, S, I

Returns:

All numpy arrays

if return_full_data

return times, S, I, Sk, Ik, SI, SS, II

else

return times, S, I

SAMPLE USE:

import networkx as nx
import EoN