SIR_prob: Transition probabilities of an SIR process

In MultiBD: Multivariate Birth-Death Processes

Description

Computes the transition pobabilities of an SIR process using the bivariate birth process representation

Usage

SIR_prob(t, alpha, beta, S0, I0, nSI, nIR, direction = c("Forward",
  "Backward"), nblocks = 20, tol = 1e-12, computeMode = 0, nThreads = 4)

Arguments

t	time
alpha	removal rate
beta	infection rate
S0	initial susceptible population
I0	initial infectious population
nSI	number of infection events
nIR	number of removal events
direction	direction of the transition probabilities (either Forward or Backward)
nblocks	number of blocks
tol	tolerance
computeMode	computation mode
nThreads	number of threads

Value

a matrix of the transition probabilities

Examples

data(Eyam)

loglik_sir <- function(param, data) {
  alpha <- exp(param[1]) # Rates must be non-negative
  beta  <- exp(param[2])
  
  if(length(unique(rowSums(data[, c("S", "I", "R")]))) > 1) {
    stop ("Please make sure the data conform with a closed population")
  }
  
  sum(sapply(1:(nrow(data) - 1), # Sum across all time steps k
             function(k) {
               log(
                 SIR_prob(  # Compute the forward transition probability matrix
                   t  = data$time[k + 1] - data$time[k], # Time increment
                   alpha = alpha, beta = beta, 
                   S0 = data$S[k], I0 = data$I[k],       # From: R(t_k), I(t_k)
                   nSI = data$S[k] - data$S[k + 1], nIR = data$R[k + 1] - data$R[k],
                   computeMode = 4, nblocks = 80         # Compute using 4 threads
                 )[data$S[k] - data$S[k + 1] + 1, 
                   data$R[k + 1] - data$R[k] + 1]        # To: R(t_(k+1)), I(t_(k+1))
               )
             }))
}

loglik_sir(log(c(3.204, 0.019)), Eyam) # Evaluate at mode

MultiBD documentation built on May 2, 2019, 11:50 a.m.