% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/epi_quantities.R
\name{final_size_general}
\alias{final_size_general}
\title{Final epidemic size under general proportional initial conditions}
\usage{
final_size_general(params, f, m_grid = NULL, I_seed = 1e-04, tol = 1e-10)
}
\arguments{
\item{params}{A \code{"seair_params"} object.}

\item{f}{A mobility density, either a function on \eqn{[0,1]} or a
numeric vector of values on \code{m_grid}.}

\item{m_grid}{Optional mobility grid used when \code{f} is numeric,
or to evaluate the integrals (default: uniform grid of 201 points).}

\item{I_seed}{Initial symptomatic fraction.}

\item{tol}{Tolerance for \code{\link{uniroot}}.}
}
\value{
A list with \code{R_inf}, \code{MR_inf}, \code{R0}, and
  \code{converged}.
}
\description{
Solves the scalar equation of Theorem 4.3 (final-size relation),
\deqn{M_R^\infty + \int_0^1 m S_0(m)\,
    \exp\!\bigl(-\beta m [ c\,(M_R^\infty - M_R^0)
                        + (\delta/\gamma_I - c)\,M_I^0 ]\bigr) dm
    \;=\; \int_0^1 m f(m)\,dm,}
allowing a nonzero initial symptomatic fraction
\eqn{I_0 = I_{\mathrm{seed}} f}, with \eqn{E_0 = A_0 = R_0 = 0}.
}
\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 <- function(m) 6 * m * (1 - m)
final_size_general(pars, f, I_seed = 0.001)

}
