Basic reproduction number under heterogeneous mixing

R0 is the spectral radius of the next generation matrix. The dominant eigenvalue is found by power iteration, which converges for a non-negative primitive matrix by Perron-Frobenius; the same theorem is why the dominant eigenvector – the stable distribution of infections across groups – can be reported with a positive sign. Homogeneous mixing collapses to R0 = c n / gamma, the closed form the tests check.

Usage

Hetmix(contact_matrix, gamma, iters = 2000, tol = 1e-14)

Arguments

contact_matrix

Square non-negative transmission matrix.

gamma

Per-group removal rates, or one shared rate.

iters

Power iteration cap.

tol

Convergence tolerance on the eigenvalue.

Value

List with estimate, R0, stable_distribution, iterations, epidemic, n, method.

Details

Formula: R0 = rho(C diag(1/gamma)).

References

Diekmann and Heesterbeek (2000), Mathematical Epidemiology of Infectious Diseases, Wiley, ch. 5; Diekmann, Heesterbeek and Metz (1990), Journal of Mathematical Biology 28(4):365-382. doi:10.1007/BF00178324

Examples

Hetmix(contact_matrix = 5L, gamma = 0.5)
#> $estimate
#> [1] 10
#> 
#> $R0
#> [1] 10
#> 
#> $stable_distribution
#> [1] 1
#> 
#> $iterations
#> [1] 2
#> 
#> $epidemic
#> [1] 1
#> 
#> $n
#> [1] 1
#> 
#> $method
#> [1] "spectral radius of K = C diag(1/gamma), Diekmann & Heesterbeek (2000) ch. 5"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"