time_bins.sir  R Documentation 
Run simulations for an SIR (susceptibleinfectedrecovered) model, on a graph
## S3 method for class 'sir' time_bins(x, middle = TRUE) ## S3 method for class 'sir' median(x, na.rm = FALSE, ...) ## S3 method for class 'sir' quantile(x, comp = c("NI", "NS", "NR"), prob, ...) sir(graph, beta, gamma, no.sim = 100)
x 
A 
middle 
Logical scalar, whether to return the middle of the time bins, or the boundaries. 
na.rm 
Logical scalar, whether to ignore 
... 
Additional arguments, ignored currently. 
comp 
Character scalar. The component to calculate the quantile of.

prob 
Numeric vector of probabilities, in [0,1], they specify the quantiles to calculate. 
graph 
The graph to run the model on. If directed, then edge directions are ignored and a warning is given. 
beta 
Nonnegative scalar. 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 
Positive scalar. The rate of recovery of an infected individual. Formally, this is the rate parameter of an exponential distribution. 
no.sim 
Integer scalar, the number simulation runs to perform. 
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.
The function sir
simulates the model.
Function time_bins
bins the simulation steps, using the
FreedmanDiaconis heuristics to determine the bin width.
Function median
and quantile
calculate the median and
quantiles of the results, respectively, in bins calculated with
time_bins
.
For sir
the results are returned in an object of class
‘sir
’, which is a list, with one element for each simulation.
Each simulation is itself a list with the following elements. They are all
numeric vectors, with equal length:
The times of the events.
The number of susceptibles in the population, over time.
The number of infected individuals in the population, over time.
The number of recovered individuals in the population, over time.
Function time_bins
returns a numeric vector, the middle or the
boundaries of the time bins, depending on the middle
argument.
median
returns a list of three named numeric vectors, NS
,
NI
and NR
. The names within the vectors are created from the
time bins.
quantile
returns the same vector as median
(but only one, the
one requested) if only one quantile is requested. If multiple quantiles are
requested, then a list of these vectors is returned, one for each quantile.
Gabor Csardi csardi.gabor@gmail.com. Eric Kolaczyk (http://math.bu.edu/people/kolaczyk/) wrote the initial version in R.
Bailey, Norman T. J. (1975). The mathematical theory of infectious diseases and its applications (2nd ed.). London: Griffin.
plot.sir
to conveniently plot the results
g < sample_gnm(100, 100) sm < sir(g, beta=5, gamma=1) plot(sm)
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