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Upper and lower bounds to linear compartmental model output

Schinaia G.

Archives of Control Sciences

1999

Vol. 9, no. 1/2

159-169

A general compartmental system is described by the following matrix form equations dx/dt=A'X+Y , where A is a compartmental matrix with its elements being constant or functions of t and/or of X. With a distance function given by d(A,B)=sup ij|a ij - b ij|, the space of compartmental matrices is a complete metric space and some important properties, such as uniform continuity over of the system solution Xt(A)=X(t), as a function of A, can be derived in the linear, autonomous, constant coefficient case. Using these properties, upper and lower bounds to the model output are thus obtained and some applications, including a linearized epidemic model, show the use of such bounds in correspondence of various level of accuracy of the model parameter estimates A={a ij} .