Calculate the equilibrium of a linear facility model
equilib(M, init, mgf = NULL)
equilib(M, init, mgf = NULL)
M |
A matrix of state transition rates between facility patient states |
init |
A vector of admission state probabilities to each state |
mgf |
The moment generating function characterizing a time-of-stay-dependent removal hazard |
A vector with the proportion of patients in each state at equilibrium
M <- rbind(c(-0.06,0.03,0),c(0.06,-0.08,0),c(0,0.05,0)) init <- c(0.95,0.05,0) mgf <- function(x, deriv=0) MGFgamma(x, rate = 0.05, shape = 2.5, deriv) equilib(M, init, mgf)
M <- rbind(c(-0.06,0.03,0),c(0.06,-0.08,0),c(0,0.05,0)) init <- c(0.95,0.05,0) mgf <- function(x, deriv=0) MGFgamma(x, rate = 0.05, shape = 2.5, deriv) equilib(M, init, mgf)
Calculate the equilibrium of a facility transmission model
facilityeq(S, C, A, R, transm, init, mgf = NULL)
facilityeq(S, C, A, R, transm, init, mgf = NULL)
S |
A matrix of state transition rates between and removal from the susceptible states in the absence of colonized individuals |
C |
A matrix of state transition rates between and removal from the colonized states |
A |
A matrix describing transitions from susceptible to colonized states at acquisition |
R |
A matrix of recovery rates: state transition rates from colonized to susceptible states |
transm |
A vector of transmission rates from each colonized state |
init |
A vector of admission state probabilities to each state |
mgf |
The moment generating function characterizing a time-of-stay-dependent removal hazard |
A vector with the proportion of patients in each state at equilibrium; the vector contains the equilibrium S states followed by C states
S <- 0 C <- rbind(c(-0.38,0),c(0.08,0)) A <- rbind(1,0) R <- cbind(0.3,0) transm <- c(0.1,0.05) init <- c(0.99,0.01,0) mgf <- function(x, deriv=0) MGFgamma(x, rate=0.2, shape=3, deriv) facilityeq(S, C, A, R, transm, init, mgf)
S <- 0 C <- rbind(c(-0.38,0),c(0.08,0)) A <- rbind(1,0) R <- cbind(0.3,0) transm <- c(0.1,0.05) init <- c(0.99,0.01,0) mgf <- function(x, deriv=0) MGFgamma(x, rate=0.2, shape=3, deriv) facilityeq(S, C, A, R, transm, init, mgf)
Calculate basic reproduction number R0
facilityR0(S, C, A, transm, initS, mgf = NULL)
facilityR0(S, C, A, transm, initS, mgf = NULL)
S |
A matrix of state transition rates between and removal from the susceptible states in the absence of colonized individuals |
C |
A matrix of state transition rates between and removal from the colonized states |
A |
A matrix describing transitions from susceptible to colonized states at acquisition |
transm |
A vector of transmission rates from each colonized state |
initS |
A vector of admission state probabilities to each susceptible state |
mgf |
The moment generating function characterizing the time-of-stay-dependent removal hazard |
A number (R0)
S <- rbind(c(-1,2),c(1,-2)) C <- rbind(c(-1.1,0),c(0.1,-0.9)) A <- rbind(c(1,0),c(0,2)) transm <- c(0.4,0.6) initS <- c(0.9,0.1) mgf <- function(x, deriv=0) MGFgamma(x, rate=0.01, shape=3.1, deriv) facilityR0(S,C,A,transm,initS,mgf)
S <- rbind(c(-1,2),c(1,-2)) C <- rbind(c(-1.1,0),c(0.1,-0.9)) A <- rbind(c(1,0),c(0,2)) transm <- c(0.4,0.6) initS <- c(0.9,0.1) mgf <- function(x, deriv=0) MGFgamma(x, rate=0.01, shape=3.1, deriv) facilityR0(S,C,A,transm,initS,mgf)
Calculate the mean length of stay for a linear facility model
meanlengthofstay(M, init, mgf)
meanlengthofstay(M, init, mgf)
M |
A matrix of state transition rates between facility patient states |
init |
A vector of admission state probabilities to each state |
mgf |
The moment generating function characterizing a time-of-stay-dependent removal hazard |
The mean length of stay
M <- rbind(c(-1.1,2),c(1,-2.2)) init <- c(0.9,0.1) mgf <- function(x, deriv=0) MGFgamma(x, rate=0.2, shape=3, deriv) meanlengthofstay(M, init, mgf)
M <- rbind(c(-1.1,2),c(1,-2.2)) init <- c(0.9,0.1) mgf <- function(x, deriv=0) MGFgamma(x, rate=0.2, shape=3, deriv) meanlengthofstay(M, init, mgf)
Evaluate the moment generating function (MGF) of the exponential distribution or a derivative of the MGF
MGFexponential(x, rate, deriv = 0)
MGFexponential(x, rate, deriv = 0)
x |
The value at which to evaluate the MGF |
rate |
The rate parameter value of the exponential distribution |
deriv |
An integer, the number of derivatives of the MGF to apply |
The number resulting from the function evaluation
# MGF of an exponential distribution, evaluated at -0.1: MGFexponential(-0.1, rate = 0.05) # Second moment of the distribution (second derivative evaluated at zero): MGFexponential(0, rate = 0.05, deriv = 2)
# MGF of an exponential distribution, evaluated at -0.1: MGFexponential(-0.1, rate = 0.05) # Second moment of the distribution (second derivative evaluated at zero): MGFexponential(0, rate = 0.05, deriv = 2)
Evaluate the moment generating function (MGF) of the gamma distribution or a derivative of the MGF
MGFgamma(x, rate, shape, deriv = 0)
MGFgamma(x, rate, shape, deriv = 0)
x |
The value at which to evaluate the MGF |
rate |
The rate parameter value of the gamma distribution |
shape |
The shape parameter values of the gamma distribution |
deriv |
An integer, the number of derivatives of the MGF to apply |
The number resulting from the function evaluation
# MGF of a gamma distributions, evaluated at -0.1: MGFgamma(-0.1, rate = 0.7, shape = 3) # Second moment of the distribution (second derivative evaluated at zero): MGFgamma(0, rate = 0.7, shape = 3, deriv = 2)
# MGF of a gamma distributions, evaluated at -0.1: MGFgamma(-0.1, rate = 0.7, shape = 3) # Second moment of the distribution (second derivative evaluated at zero): MGFgamma(0, rate = 0.7, shape = 3, deriv = 2)
Evaluate the moment generating function (MGF) of the mixed gamma distribution or a derivative of the MGF
MGFmixedgamma(x, prob, rate, shape, deriv = 0)
MGFmixedgamma(x, prob, rate, shape, deriv = 0)
x |
The value at which to evaluate the MGF |
prob |
A vector of probabilities of following each gamma distribution in the mixture |
rate |
A vector of rate parameter values for each gamma distribution in the mixture |
shape |
A vector of shape parameter values for each gamma distribution in the mixture |
deriv |
An integer, the number of derivatives of the MGF to apply |
The number resulting from the function evaluation
# MGF of a 40/60 mixture of two gamma distributions, evaluated at -0.1: MGFmixedgamma(-0.1, prob = c(0.4,0.6), rate = c(0.4,0.7), shape = c(0.5,3)) # Second moment of the distribution (second derivative evaluated at zero): MGFmixedgamma(0, prob = c(0.4,0.6), rate = c(0.4,0.7), shape = c(0.5,3), deriv = 2)
# MGF of a 40/60 mixture of two gamma distributions, evaluated at -0.1: MGFmixedgamma(-0.1, prob = c(0.4,0.6), rate = c(0.4,0.7), shape = c(0.5,3)) # Second moment of the distribution (second derivative evaluated at zero): MGFmixedgamma(0, prob = c(0.4,0.6), rate = c(0.4,0.7), shape = c(0.5,3), deriv = 2)