4Compartmental Models

4.1 Introduction

In this chapter we introduce the notion of compartmental modeling, which is widely used in the fields of biology, epidemiology, pharmacokinetics, pharmacodynamics, physiology, and chemical or nuclear reactions [13, 14, 24, 36]. Compartmental modeling is a modeling method that decomposes a system into homogeneous compartments, where each compartment may represent a population of like individuals, material, chemicals, or other quantities [28].

Figure 4.1 is a representation of a simple two‐compartment model. The arrows represent flows or transfers between compartments. We assume that the rate of change of the state x left-parenthesis t right-parenthesis in each compartment is equal to the input flow minus the output flow. The governing equations of this model are therefore

StartLayout 1st Row 1st Column ModifyingAbove x With dot Subscript 1 2nd Column equals 3rd Column minus k 1 x 1 plus k 2 x 2 2nd Row 1st Column ModifyingAbove x With dot Subscript 2 2nd Column equals 3rd Column k 1 x 1 minus k 2 x 2 period EndLayout

The coefficients k 1 and k 2 may be constant, time varying, or functions of the states x 1 and x 2. Therefore, this model is ...

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