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

In demogR: Analysis of Age-Structured Demographic Models

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?

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.

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

...

Author(s)

James Holland Jones

References

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

See Also

see leslie.matrix

Examples

## 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)

Example output

[1] 2.287108
[[1]]
[1] 2.287108

[[2]]
          [,1]    [,2]   [,3] [,4] [,5]
[1,] 1.0000000 0.00000 0.0000 0.00    0
[2,] 0.7700000 1.00000 0.0000 0.00    0
[3,] 0.7315000 0.95000 1.0000 0.00    0
[4,] 0.7168700 0.93100 0.9800 1.00    0
[5,] 0.6953639 0.90307 0.9506 0.97    1

demogR documentation built on May 1, 2019, 10:56 p.m.