Author: Klinkenberg, Don; Fraser, Christophe; Heesterbeek, Hans
Title: The Effectiveness of Contact Tracing in Emerging Epidemics Document date: 2006_12_20
ID: 1n0rg5vd_38
Snippet: Even though the matrix is infinitely large, we conjecture from all observed numerical calculations that the positive elements k j+1,j converge in the sense that |k j+1,j 2k j+2,j+1 |R0 as jR'. Therefore, for numerical evaluation we 'closed' the matrix to an (n+1) 2 matrix with k nn = k n+1,n . For the four special cases, R q could be calculated numerically in MathematicaH, but for other cases considered, the entries of the matrix had to be determ.....
Document: Even though the matrix is infinitely large, we conjecture from all observed numerical calculations that the positive elements k j+1,j converge in the sense that |k j+1,j 2k j+2,j+1 |R0 as jR'. Therefore, for numerical evaluation we 'closed' the matrix to an (n+1) 2 matrix with k nn = k n+1,n . For the four special cases, R q could be calculated numerically in MathematicaH, but for other cases considered, the entries of the matrix had to be determined by numerical simulation. Analysis of single-step tracing with delay could be done by calculating R from the next-generation matrix, as for the model without delay (see Supporting Information for all details).
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