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This submodule deals with epidemic simulation. We start with a quick list ofthe functions with links to the individual functions. A brief description isbelow.
| fast_SIR(G, tau, gamma[, initial_infecteds, …]) | fast SIR simulation for exponentially distributed infection and recovery times |
| fast_nonMarkov_SIR(G[, trans_time_fxn, …]) | A modification of the algorithm in figure A.3 of Kiss, Miller, & Simon to allow for user-defined rules governing time of transmission. |
| fast_SIS(G, tau, gamma[, initial_infecteds, …]) | Fast SIS simulations for epidemics on weighted or unweighted networks, allowing edge and node weights to scale the transmission and recovery rates. |
| fast_nonMarkov_SIS(G[, trans_time_fxn, …]) | Similar to fast_nonMarkov_SIR. |
| Gillespie_SIR(G, tau, gamma[, …]) | Performs SIR simulations for epidemics. |
| Gillespie_SIS(G, tau, gamma[, …]) | Performs SIS simulations for epidemics on networks with or without weighted edges. |
| Gillespie_Arbitrary(G, …[, tmin, tmax, …]) | Calls Gillespie_simple_contagion. |
| Gillespie_simple_contagion(G, …[, tmin, …]) | Performs simulations for epidemics, allowing more flexibility than SIR/SIS. |
| Gillespie_complex_contagion(G, …[, tmin, …]) | Initially intended for a complex contagion. |
| basic_discrete_SIR(G, p[, …]) | Performs simple discrete SIR simulation assuming constant transmission probability p. |
| basic_discrete_SIS(G, p[, …]) | Does a simulation of the simple case of all nodes transmitting with probability p independently to each susceptible neighbor and then recovering. |
| discrete_SIR(G[, test_transmission, args, …]) | Simulates an SIR epidemic on G in discrete time, allowing user-specified transmission rules |
| percolate_network(G, p) | Performs percolation on a network G with each edge persisting with probability p |
| directed_percolate_network(G, tau, gamma[, …]) | performs directed percolation, assuming that transmission and recovery are Markovian |
| nonMarkov_directed_percolate_network_with_timing(G, …) | Performs directed percolation on G for user-specified transmission time and recovery time distributions. |
| nonMarkov_directed_percolate_network(G, xi, …) | performs directed percolation on a network following user-specified rules. |
| estimate_SIR_prob_size(G, p) | Uses percolation to estimate the probability and size of epidemics assuming constant transmission probability p |
| estimate_SIR_prob_size_from_dir_perc(H) | Estimates probability and size of SIR epidemics for an input network after directed percolation |
| estimate_directed_SIR_prob_size(G, tau, gamma) | Predicts probability and attack rate assuming continuous-time Markovian SIR disease on network G |
| estimate_nonMarkov_SIR_prob_size_with_timing(G, …) | estimates probability and size for user-input transmission and recovery time functions. |
| estimate_nonMarkov_SIR_prob_size(G, xi, …) | Predicts epidemic probability and size using nonMarkov_directed_percolate_network. |
| get_infected_nodes(G, tau, gamma[, …]) | Finds all eventually infected nodes in an SIR simulation, through a percolation approach |
| percolation_based_discrete_SIR(G, p[, …]) | perfoms a simple SIR epidemic but using percolation as the underlying method. |
Event-based algorithms:
These algorithms use an efficient approach to simulate epidemics. fast_SIRand fast_SIS assume constant transmission and recovery rates, whilefast_nonMarkov_SIR and fast_nonMarkov_SIS allow the user to specifymore detailed rules for transmission.
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These algorithms simulate epidemics assuming constant transmission andrecovery rates. They are commonly used, but in many cases are slower thanthe event driven methods. I do not see evidence that they are eversignificantly faster. It is not very practical to get away from theconstant rate assumptions so I prefer to avoid them. However,Gillespie_simple_contagion allows the user to do SEIR, SIRS, or any of a numberof other more exotic “simple contagion” scenarios that are not in the event-drivencode. Gillespie_complex_contagion handles complex contagions, in which anindividual requires multiple partners to have a given state before it changesstatus. For legacy reasons, Gillespie_Arbitrary is included, it simply callsGillespie_simple_contagion, and will be removed in future versions.
Discrete-time algorithms
These algirthms are appropriate for where we separate infection intogenerations. We assume infection lasts a single time step. The basic_*algorithms assume that transmission occurs with probability p for all edges.In contrast discrete_SIR allows for very general user-specifiedtransmission rules.
Percolation-based approaches
There is a close relation between percolation and SIR disease which isdescribed in Chapter 6 of the book. Many of these algorithms are relatedto demonstrating the equivalence as outlined in the book, and are not reallythe most efficient way to simulate an epidemic. However, these algorithmswill be useful for estimating probability and size of epidemics.
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