demogR (version 0.6.0)

calc.ro: Caclulate net reproduction number from a demographic projection matrix

Description

Calculate the net reproduction number (\(R_0\)) from an age or stage-classified demographic projection matrix.

Usage

calc.ro(A, N.out = FALSE)

Arguments

A

A demographic projection matrix

N.out

Return the fundamental matrix (N) of the Markov chain?

Value

If the (default) option N.out=FALSE is used, the net reproduction number is returned as a single value. If N.out=TRUE, the returned value is a list of two items:

ro

Net reproduction number

N

Fundamental matrix

...

Details

Calculates the net reproduction number (\(R_0\)) from an age or stage-classified demographic projection matrix by first decomposing the k x k projection matrix A into two component matrices, T and F. T collects the transitions between life-cycle stages while F collects the fertility transitions. For an age-classified Leslie matrix, T will contain only the sub-diagonal of A and F will contain only the first row of A. The fundamental matrix is given by \(N = (I-T)^{-1}\), where I is a k x k identity matrix. \(R_0\) is the leading eigenvalue of the matrix FN.

References

Caswell, H. 2001. Matrix population models: construction, analysis, and interpretation, Second edition. Sinauer, Sunderland, Massachusetts, USA.

See Also

see leslie.matrix

Examples

# NOT RUN {
## Create a Leslie matrix
Px <- c(0.77, 0.95, 0.98, 0.97)
Fx <- c(0,0,1,1.2,1)
L <- odiag(Px,-1)
L[1,] <- Fx
## Calculate R_0
calc.ro(L)
## look at the fundamental matrix
calc.ro(L, N.out=TRUE)
# }