Some equivalent compartmental models |
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Authors: | Gilbert G Walter |
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Institution: | University of Wisconsin, Milwaukee Wisconsin 53201 USA |
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Abstract: | Compartmental models with strongly connected digraphs always have a stable equilibrium solution. Each such model may be reduced by a sequence of matrix operations to a mammilary system with the same equilibrium solution. It may also be reduced by a sequence of operations on the digraph. It may then be further reduced to a model whose digraph is a 2-cycle with the same mean first passage time m. If this m is taken as an indicator of the relative stability, then the latter is independent of the complexity as measured by the number of arcs per vertex. In a number of special cases the index m is related to the eigenvalues of the matrix. It is shown to have a simple relation to other time parameters as well. |
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