SimInf (version 11.1.0)

SIR: Create an SIR model

Description

Create an SIR model to be used by the simulation framework.

Usage

SIR(u0, tspan, events = NULL, beta = NULL, gamma = NULL)

Value

A SimInf_model of class SIR

Arguments

u0

A data.frame with the initial state in each node, i.e., the number of individuals in each compartment in each node when the simulation starts (see ‘Details’). The parameter u0 can also be an object that can be coerced to a data.frame, e.g., a named numeric vector will be coerced to a one row data.frame.

tspan

A vector (length >= 1) of increasing time points where the state of each node is to be returned. Can be either an integer or a Date vector.

• If integer: Represents the specific time points (e.g., days, hours) at which to record the state.

• If Date: Coerced to a numeric vector representing the day of the year (1–366) relative to the first date in the vector. The original Date objects are preserved as names for the numeric vector, facilitating time-series plotting.

events

a data.frame with the scheduled events, see SimInf_model.

beta

A numeric vector with the transmission rate from susceptible to infected. Each node can have a different beta value. The vector must have length 1 or nrow(u0). If the vector has length 1 but the model contains more nodes, the beta value is repeated for all nodes.

gamma

A numeric vector with the recovery rate from infected to recovered. Each node can have a different gamma value. The vector must have length 1 or nrow(u0). If the vector has length 1 but the model contains more nodes, the gamma value is repeated for all nodes.

Details

The SIR model is a compartmental model for infectious diseases that divides the population into three states: Susceptible, Infected, and Recovered. It assumes that individuals gain permanent immunity after recovery.

The model is defined by two state transitions: $$S \stackrel{\beta S I / N}{\longrightarrow} I$$ $$I \stackrel{\gamma I}{\longrightarrow} R$$

where \(\beta\) is the transmission rate, \(\gamma\) is the recovery rate, and \(N = S + I + R\) is the total population size in each node. Here, \(S\), \(I\), and \(R\) represent the number of susceptible, infected, and recovered individuals in that specific node.

The argument u0 must be a data.frame with one row for each node with the following columns:

S

The number of susceptible individuals in each node

I

The number of infected individuals in each node

R

The number of recovered individuals in each node

See Also

SIR for the class definition. SEIR, SIS, SISe, SISe3 and SISe_sp for other predefined models. mparse for creating custom models. run for running the simulation. trajectory, prevalence and plot for post-processing and visualization.

Examples

## Create an SIR model object.
model <- SIR(
  u0 = data.frame(S = 99, I = 1, R = 0),
  tspan = 1:100,
  beta = 0.16,
  gamma = 0.077
)

## Run the SIR model with a fixed seed for reproducibility.
result <- run(model, seed = 22)

## Plot the distribution of susceptible, infected and recovered
## individuals.
plot(result)