EoN.SIR_compact_effective_degree¶
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EoN.
SIR_compact_effective_degree
(Skappa0, I0, R0, SI0, tau, gamma, tmin=0, tmax=100, tcount=1001, return_full_data=False)[source]¶ Encodes system (5.43) of Kiss, Miller, & Simon. Please cite the book if using this algorithm.
- dot{S}_kappa = <I> [-(tau+gamma) kappa S_kappa
- gamma(kappa+1)S_{kappa+1}
- [dot{SI}] = -(tau+gamma)[SI]
- tau(<I> - 2 <I>^2) sum_{kappa} kappa(kappa-1) S_kappa
dot{R} = gamma I <I> = [SI]/sum_kappa kappa S_kappa S = sum_kappa S_kappa I = N - S - R
Arguments: - Skappa0 : numpy array
from S_0(0) up to S_kappamax(0) of number susceptible with each effective degree Skappa = number of nodes that are susceptible and have kappa non-recovered neighbors
- I0 number
- number of infected individuals at time 0
- R0 number
- initial number recovered
- SI0 number
- initial number of SI 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
- tells whether to just return times, S, I, R or all calculated data.
Returns: - if return_full_data==False
times np.array of times
S np.array of number susceptible
I np.array of number infected
R np.array of number recovered
- else
times as before
S number susceptible
I number infected
R number recovered
- SI S_{s,i}
- number of SI edges