seir.auxiliary function

Auxiliary Functions for the SEIR Model without Forcing

Calculate the basic reproduction number, endemic equilibrium, and Jacobian matrix of the SEIR model without forcing.

seir.R0      (beta, nu = 0, mu = 0, sigma = 1, gamma = 1, delta = 0,
              m = 1L, n = 1L, N = 1)
seir.ee      (beta, nu = 0, mu = 0, sigma = 1, gamma = 1, delta = 0,
              m = 1L, n = 1L, N = 1)
seir.jacobian(beta, nu = 0, mu = 0, sigma = 1, gamma = 1, delta = 0,
              m = 1L, n = 1L)

Arguments

• beta, nu, mu, sigma, gamma, delta: non-negative numbers. beta, nu, and mu are the rates of transmission, birth, and natural death. m*sigma, n*gamma, and delta are the rates of removal from each latent, infectious, and recovered compartment.
• m: a non-negative integer indicating a number of latent stages.
• n: a positive integer indicating a number of infectious stages.
• N: a non-negative number indicating a population size for the (nu == 0 && mu == 0) case.

Returns

seir.R0 returns a numeric vector of length 1. seir.ee

returns a numeric vector of length 1+m+n+1. seir.jacobian

returns a function of one argument x (which must be a numeric vector of length 1+m+n+1) whose return value is a square numeric matrix of size length(x).

Details

If $mu = 0 and nu = 0$, then the basic reproduction number is computed as

and the endemic equilibrium is computed as

where $w$ is chosen so that the sum is $N$.

If $mu > 0 and nu > 0$, then the basic reproduction number is computed as

and the endemic equilibrium is computed as

where $w$ is chosen so that the sum is $nu / mu$, the population size at equilibrium, and $a = 1 + mu / (m * sigma)$ and $b = 1 + mu / (n * gamma)$.

Currently, none of the functions documented here are vectorized. Arguments must have length 1.

See Also

seir, for the system of ordinary differential equations on which these computations are predicated.