% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/epi_quantities.R
\name{R0_seair}
\alias{R0_seair}
\title{Basic reproduction number of the mobility-based SEAIR model}
\usage{
R0_seair(params, f, m_grid = NULL)
}
\arguments{
\item{params}{A \code{"seair_params"} object.}

\item{f}{A function returning the density \eqn{f(m)} on \eqn{[0,1]},
or a numeric vector of \eqn{f} values evaluated on \code{m_grid}.}

\item{m_grid}{Mobility grid (used only if \code{f} is numeric).}
}
\value{
The basic reproduction number \eqn{\mathcal{R}_0}.
}
\description{
For a mobility distribution \eqn{f} on \eqn{(0,1)}, the basic
reproduction number at the disease-free equilibrium is
\deqn{\mathcal{R}_0 \;=\; \beta\,c\,\langle m^2 f \rangle,}
where \eqn{c} is as in \code{\link{c_effective}} and
\eqn{\langle m^2 f \rangle = \int_0^1 m^2 f(m)\,dm}.
}
\examples{
pars <- seair_params(beta = 1.5, sigma = 0.3, kappa = 0.2,
                     gamma_A = 0.1, gamma_I = 0.13,
                     alpha = 0.5, delta = 0.3)

## f given as a function (normalised automatically by the caller).
f <- function(m) 6 * m * (1 - m)    # Beta(2, 2) density on [0, 1]
R0_seair(pars, f)

## f given as values on a grid.
m <- seq(0, 1, length.out = 101)
R0_seair(pars, f(m), m_grid = m)

}
