SIRD-GA with piecewise-constant transmission, fitted to cases and deaths

Maximum likelihood for the SIRD-GA model in which the transmission rate is constant within blocks of observation intervals, \(\lambda(t)=\lambda_b\) for \(t\) in block \(b\), while the removal rates \(\gamma\), \(\alpha\), the initial infectious fraction, the case reporting probability and the two noise scales are shared. Parameters listed in fixed are held at the given values (e.g. a profile over p).

Usage

sird_ga_fit_tv(
  cases = NULL,
  deaths = NULL,
  N,
  blocks,
  use = c("both", "cases", "deaths"),
  start,
  fixed = list(),
  q = 1,
  p_max = 0.999,
  Delta = 1,
  nsub = 10L,
  maxit = 3000
)

Arguments

cases, deaths, N, use, Delta, nsub

See sird_ga_loglik_inc().

blocks

Integer vector, one entry per observation interval, giving the block of each interval (1, ..., B).

start

Named list of starting values for gamma, alpha, i0, p, tau2, tau2_d and a vector lambda of length B.

fixed

Named list of parameters held fixed (any of gamma, alpha, i0, p, tau2, tau2_d); q (default 1) is always fixed.

q

Death reporting probability (fixed).

p_max

Upper bound for p.

maxit

Iteration limit.

Value

A list with lambda (per block), theta, loglik, par, hessian, R_t (per interval, \(\lambda(t)s(t)/(\gamma+\alpha)\)) and the full Kalman output kf.