SPOT (version 2.1.10)

modelMarkovChain: modelMarkovChain

Description

Modeling continuous time Markov chains (MarkovChain) models using SIR models.

Usage

modelMarkovChain(x, days, N, n = 3)

Arguments

x

vector of three parameters. Used for parametrizing the MarkovChain model.

p

num [0;1] proportion of confirmed cases

beta

num A numeric vector with the transmission rate from susceptible to infected where 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 in all nodes.

gamma

num A numeric vector with the recovery rate from infected to recovered where 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 beta value is repeated in all nodes.

days

number of simulation steps, usually days (int). It will be used to generate (internally) a vector (length >= 1) of increasing time points where the state of each node is to be returned.

N

population size

n

number of nodes to be evaluated in the SIR model

Value

data.frame of days obs. of 4 variables:

t

num 0 1 2 3 4 5 6 7 8 9 ... (timesteps)

X1

num 1704 1490 1275 1069 880 ... (susceptible)

X2

num 1000 1178 1351 1509 1646 ... (infected)

X3

num num 0 36.3 78.5 126.2 178.8 ... (recovered)

Details

SIR considers three compartments: S (susceptible), I (infected), and R (recovered). Using the parameter vector x, the population size N, and the number of days (prediction horizon), the SIR model parameters are determined as follows. N denotes the population size. First: S, the number of susceptible in each node, will be calculated as N - I - R, where I is the number of infected in each node, and R is the number of recovered in each node. Then, the data frame `u0` is set up: u0 = data.frame(S , I , R). `u0` contains the initial number of individuals in each compartment in every node. An integer matrix (Ncomp <U+00D7> Nnodes) is used for storing `u0` information. The timespan is calculated as tspan = 1:days. The SIR is set up and run, using run.

Examples

# NOT RUN {
require("SimInf")
data <- preprocessInputData(regionTrain, regionPopulation)
regionData <- data[[1]]
N <- attr(regionData, "regionPopulation")
# N_curr <- max(regionData$confirmed)
p <- 0.01
beta <- 0.1
gamma <- 0.01
# parameter vector for the SIR model: (p, beta, gamma)
x <- c(p, beta, gamma)
# Every row in the data represents one day:
days <- nrow(regionData)
modelMarkovChain(x = x, days = days, N = N)
# }