Multi-start SIRD-GA fitting, with a practical-identifiability summary

Fits the SIRD-GA model from several starting points spanning a range of assumed mean infectious periods, and reports all converged optima sorted by log-likelihood. This is useful because, on real surveillance data, the SIRD-GA log-likelihood can have a near-flat ridge along which lambda trades off against gamma + alpha while R0 and the shape of the fitted curve stay essentially unchanged — a known weak-identifiability feature of SIR/SIRD models fit to incidence-only series (the removal rate is identified mainly through its sum with the transmission rate and the curve's inflection timing, not independently). Reporting the single best-fitting optimum without checking for this ridge can be misleading; this function makes the ridge (if present) visible.

Usage

sird_ga_fit_multistart(
  y,
  N,
  Delta = 1,
  r0_guess = 1.1,
  infectious_period_days = c(2, 3, 4, 5, 7, 10),
  alpha_frac = 0.1,
  p0 = 0.9,
  tau2_0 = 1,
  i0_0 = 1e-04,
  ...
)

Arguments

y

Numeric vector of observed infectious counts, y_0, ..., y_n.

N

Population size.

Delta

Time step between observations.

r0_guess

Starting guess for \(R_0\) (used to scale lambda across starts, together with each candidate infectious period).

infectious_period_days

Numeric vector of candidate mean infectious periods \(1/(\gamma+\alpha)\) (in days) to start from (default spans 2-10 days, covering typical respiratory-infection priors).

alpha_frac

Fraction of the total removal rate gamma + alpha assigned to alpha at each starting point (default 0.1).

p0, tau2_0, i0_0

Starting values shared across all starts for p, tau2 and i0.

...

Further arguments passed to sird_ga_fit().

Value

A list with results (a list of sird_ga_fit() outputs, one per start, in the same order as infectious_period_days), summary (a data frame with the starting infectious period, final log-likelihood, R0 and key parameter estimates for each start, sorted best-first) and best (the single best-fitting result).