Solve the SIRD-GA state-space transition quantities

Jointly solves the deterministic SIRD trajectory \(x(t)\) and the fundamental (sensitivity) matrix of the linearised dynamics in a single deSolve::ode() call spanning the whole observation window, using a reset event that sets the fundamental matrix back to the identity at the start of every observation interval. This gives the same locally-anchored resolvent \(\Phi(s, t_{k-1})\) as restarting the solver once per interval (and the same numerical stability — the matrix never has to span more than one interval, which matters for long series), while paying the fixed per-call overhead of deSolve::ode() only once instead of n times. This is the single biggest cost in repeated likelihood evaluation (MLE optimisation, bootstrap), so the single-call form is the default implementation.

Usage

sird_ga_transition(times, x0, parms, n_sub = 10L)

Arguments

times

Numeric vector of observation times, t_0 < t_1 < ... < t_n (typically 0:n).

x0

Initial state c(s0, i0, r0) at times[1].

parms

Named list/vector with lambda, gamma, alpha.

n_sub

Number of internal subdivisions per observation interval, used for the sird_ga_Qk() quadrature. Defaults to 10 (even, required by Simpson's rule).

Value

A list of class sird_ga_transition with components x_obs (matrix of states at t_0, ..., t_n), segments (one list per interval, with fine-grid t, x and P, P[,,1] always the identity), and parms.