I'm working on finding influential nodes in complex networks using R programming. I want to use degree centrality which means the number of neighbors a node has in a graph. I have a graph and the degree centrality of each node. Now I want to know how many nodes will be infected within a specified time when we start to spread the virus from each node. according to my studies I should use SIR(susceptible, infected, recovered) epidemic model which I found in "igraph" package, the problem is that I can't specify the starting node. It seems that this functions works based on SIR equations:
s'= -(beta)SI
I' = (beta)SI - (gamma)I
R' = (gamma)I
where beta is infection parameter and gamma is recovery parameter. here is the igraph SIR code:
function (graph, beta, gamma, no.sim = 100)
{
if (!is_igraph(graph)) {
stop("Not a graph object")
}
beta <- as.numeric(beta)
gamma <- as.numeric(gamma)
no.sim <- as.integer(no.sim)
on.exit(.Call("R_igraph_finalizer", PACKAGE = "igraph"))
res <- .Call("R_igraph_sir", graph, beta, gamma, no.sim,
PACKAGE = "igraph")
class(res) <- "sir"
res
}
It seems that most of the work is being done in "R_igraph_sir" but I cant find such a function in that package. Is there any way to set the starting node?
It seems like you'd like to have a SIR model where you are able to set the initially infected node by monkeypatching the existing R code. Since the R package is compiled from C code this might be tough depending on your programming experience and in general monkeypatching isn't recommended, if nothing else then because you will lose your code the minute you update your igraph package.
Instead you can relatively easily implement this yourself using the igraph package. Below is an untested implementation in python that should be easibly ported to R.
The first step infects any node in the graph adjacent to an infected node with a probability of beta
After infection stage any infected node can be removed from the graph with a probability of gamma
After the given number of timesteps you find the number of effected nodes as the size of the infected_nodes array. This won't count removed nodes, so if you want the total number of infected over the entire simulation you put in a counter that increments each time you infect a node
infected_nodes = []
# Set the infection rate
beta = 0.1
# Set the removal rate
gamma = 0.1
# Set how many timesteps you want to pass through
n_timesteps = 100
# Start from the node you have chosen using edge centrality
infected_nodes.append(chosen_node)
for _ in n_timesteps:
# Infection stage
for node in infected_nodes:
for neighbor in igraph.neighborhood(graph, node):
# random.random simply returns a number between [0,1)
if random.random() < beta:
infected_nodes.append(neighbor)
# Removal stage
infected_survivors = []
for node in infected_nodes:
if random.random() < gamma:
graph = igraph.delete_vertices(graph, node)
else:
infected_survivors.append(node)
infected_nodes = infected_survivors
Some aberdabeis:
n neighbors per turn you will need to take a size n random sample of the neighbors instead of iterating over all of them.