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SEI.R
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SEI.R
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#' Susceptible-Exposed-Infected Model
#'
#' @inherit SI_ode
#' @export
#'
#' @examples
#' ##Model Input
#' S_0 <- 989
#' E_0 <- 10
#' I_0 <- 1
#' beta <- 3
#' gamma = 1/2
#'
#' parameters <- c(beta = beta, gamma = gamma)
#' inits <- c(S = S_0, E = E_0, I = I_0)
#'
#' SEI_ode(1, inits, parameters)
SEI_ode <- function(t, x, params) {
## Specify model compartments
S <- x[1]
E <- x[2]
I <- x[3]
with(as.list(params),{
## Specify total population
N = S + E + I
## Derivative Expressions
dS = -beta * S * I / N
dE = +beta * S * I / N - gamma * E
dI = +gamma * E
## output
derivatives <- c(dS, dE, dI)
list(derivatives)
})
}
#' Susceptible-Exposed-Infected Model with Simple Demographics
#' @inherit SI_ode
#' @export
#'
#' @examples
#' ##Model Input
#' S_0 <- 989
#' E_0 <- 10
#' I_0 <- 1
#' beta <- 3
#' gamma <- 1/2
#' mu <- 1/81
#'
#' parameters <- c(beta = beta, gamma = gamma, mu = mu)
#' inits <- c(S = S_0, E = E_0, I = I_0)
#'
#' SEI_demographics_ode(1, inits, parameters)
SEI_demographics_ode <- function(t, x, params) {
## Specify model compartments
S <- x[1]
E <- x[2]
I <- x[3]
with(as.list(params),{
## Specify total population
N = S + E + I
## Derivative Expressions
dS = -beta * S * I / N - mu * S + mu * N
dE = +beta * S * I / N - gamma * E - mu * E
dI = +gamma * E - mu *I
## output
derivatives <- c(dS, dE, dI)
list(derivatives)
})
}