igraph Reference Manual

For using the igraph C library

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Chapter 10. Games on graphs

1. Epidemic models

1. Epidemic models

1.1. igraph_sir — Performs a number of SIR epidemics model runs on a graph.
1.2. igraph_sir_t — The result of one SIR model simulation.
1.3. igraph_sir_destroy — Deallocates memory associated with a SIR simulation run.

1.1. igraph_sir — Performs a number of SIR epidemics model runs on a graph.

igraph_error_t igraph_sir(const igraph_t *graph, igraph_real_t beta,
               igraph_real_t gamma, igraph_integer_t no_sim,
               igraph_vector_ptr_t *result);

The SIR model is a simple model from epidemiology. The individuals of the population might be in three states: susceptible, infected and recovered. Recovered people are assumed to be immune to the disease. Susceptibles become infected with a rate that depends on their number of infected neighbors. Infected people become recovered with a constant rate. See these parameters below.

This function runs multiple simulations, all starting with a single uniformly randomly chosen infected individual. A simulation is stopped when no infected individuals are left.

Arguments: 

graph:

The graph to perform the model on. For directed graphs edge directions are ignored and a warning is given.

beta:

The rate of infection of an individual that is susceptible and has a single infected neighbor. The infection rate of a susceptible individual with n infected neighbors is n times beta. Formally this is the rate parameter of an exponential distribution.

gamma:

The rate of recovery of an infected individual. Formally, this is the rate parameter of an exponential distribution.

no_sim:

The number of simulation runs to perform.

result:

The result of the simulation is stored here, in a list of igraph_sir_t objects. To deallocate memory, the user needs to call igraph_sir_destroy on each element, before destroying the pointer vector itself using igraph_vector_ptr_destroy_all().

Returns: 

Error code.

Time complexity: O(no_sim * (|V| + |E| log(|V|))).

1.2. igraph_sir_t — The result of one SIR model simulation.

typedef struct igraph_sir_t {
    igraph_vector_t times;
    igraph_vector_int_t no_s, no_i, no_r;
} igraph_sir_t;

Data structure to store the results of one simulation of the SIR (susceptible-infected-recovered) model on a graph. It has the following members. They are all (real or integer) vectors, and they are of the same length.

Values: 

times:

A vector, the times of the events are stored here.

no_s:

An integer vector, the number of susceptibles in each time step is stored here.

no_i:

An integer vector, the number of infected individuals at each time step, is stored here.

no_r:

An integer vector, the number of recovered individuals is stored here at each time step.

1.3. igraph_sir_destroy — Deallocates memory associated with a SIR simulation run.

void igraph_sir_destroy(igraph_sir_t *sir);

Arguments: 

sir:

The igraph_sir_t object storing the simulation.

← Chapter 9. Graph generators Chapter 11. Vertex and edge selectors and sequences, iterators →