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SEIR Compartmental Forward Model

Source: R/ode_templates.R
seir_forward_model.Rd

A ready-to-use ode_forward_model() specialisation for the classic Susceptible-Exposed-Infectious-Recovered epidemic model on a closed population (Anderson & May 1991). The four states evolve as $$\dot S = -\beta S I / N,\quad \dot E = \beta S I / N - \sigma E,$$ $$\dot I = \sigma E - \gamma I,\quad \dot R = \gamma I,$$ with transmission rate \(\beta\), latency rate \(\sigma\) (mean incubation \(1/\sigma\)), and recovery rate \(\gamma\) (mean infectious period \(1/\gamma\)). The basic reproduction number is \(R_0 = \beta / \gamma\).

Usage

seir_forward_model(
  times,
  n_pop = 1000,
  i0 = 1,
  solver = c("rk4", "desolve"),
  n_steps = 10L,
  ...
)

Arguments

times

Numeric vector of strictly increasing observation times (days), length at least two. The first entry is the outbreak start.

n_pop

Numeric. Total (closed) population size. Default 1000.

i0

Numeric. Initial infectious count at times[1]. Default 1. Must be positive and below n_pop.

solver

Character. "rk4" (default) or "desolve", as in ode_forward_model().

n_steps

Integer. Fixed RK4 sub-steps between observation times (default 10L).

...

Further policy arguments forwarded to pesto_forward_model() via ode_forward_model().

Value

A pesto_forward_model() S7 object with param_names c("beta", "sigma", "gamma") and n_obs = length(times) - 1L, emitting the infectious prevalence trajectory.

Details

The calibration parameters are beta, sigma, and gamma. The population size n_pop and the initial infectious count i0 are fixed structural constants of the template (an outbreak seeded with i0 infectious individuals, n_pop - i0 susceptible, and nobody exposed or recovered). By default the forward map returns the infectious prevalence \(I(t)\) at every time after the first – the compartment a case-count series tracks – so the object calibrates directly against an observed epidemic curve through pesto_ies_callback(). Supply a custom observe through ode_forward_model() to read a different compartment (for example the incidence \(\sigma E\)).

References

Anderson, R. M. & May, R. M. (1991). Infectious Diseases of Humans: Dynamics and Control. Oxford University Press.

See also

ode_forward_model() for the generic builder; crop_growth_forward_model() for the crop template; pesto_ies_callback() for calibration.

Examples

# Simulate an outbreak curve at a known (beta, sigma, gamma).
times <- seq(0, 60, by = 5)
fm <- seir_forward_model(times = times, n_pop = 1000, i0 = 1)
truth <- matrix(c(0.6, 0.2, 0.1), nrow = 1L,
                dimnames = list(NULL, c("beta", "sigma", "gamma")))
round(as.numeric(pesto_evaluate(fm, truth)), 1)
#>  [1]   1.6   4.2  11.2  29.4  72.5 156.3 265.4 333.1 321.0 258.8 187.5 127.5