EoN.SIR_homogeneous_pairwise

EoN.SIR_homogeneous_pairwise(S0, I0, R0, SI0, SS0, n, tau, gamma, tmin=0, tmax=100, tcount=1001, return_full_data=False)

Encodes System (4.11) of Kiss, Miller, & Simon. Please cite the book if using this algorithm.

In the text this is often referred to as the “mean-field model closed at the level of triples”

[dot{S}] = - tau [SI] [dot{I}] = au [SI] - gamma [I] [dot{R}] = gamma [I] ; [R] = N-[S]-[I] [dot{SI}] = -gamma [SI]+ au ((n-1)/n) [SI]([SS]-[SI])/[S]

• au [SI]

[dot{SS}] = - 2 au ((n-1)/n) [SI][SS]/[S]

conserved quantities: [S]+[I]+[R] also

[SS]+[II]+[RR] + 2([SI] + [SR] + [IR])

Arguments:

S0 float

Initial number susceptible

I0 float

Initial number infected

R0 float

Initial number recovered

SI0 float

Initial number of SI edges

SS0 float

Initial number of SS edges

n float

Degree of nodes

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)

tells whether to just return times, S, I, R or all calculated data. if True, then returns times, S, I, R, SI, SS

Returns:

if return_full_data is True:

times, S, I, R, SI, SS

if return_full_data is False:

**times, S, I, R **

SAMPLE USE:

import networkx as nx
import EoN
S0 = 990
I0 = 10
R0 = 1
SI0 = 45
SS0 = 4900
n = 5
tau = 1
gamma = 2
t, S, I, R = EoN.SIR_homogeneous_pairwise(S0, I0, R0, SI0, SS0, n, tau, gamma,
                                            tmax = 20)