Exploring The Componentwise Absolute Stability Of Endemic Epidemic Systems Via SIR Models
- Authors
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Mihail Voicu
Technical University "Gh. Asachi" of Iasi, Automatic Control and Industrial Informatics Department
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Octavian Pastravanu
Technical University "Gh. Asachi" of Iasi, Automatic Control and Industrial Informatics Department
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- Abstract
- Results of previous work on componentwise asymptotic stability (characterizations based on the flow-invariance method) are applied for the study of a class of bilinear differential equations, describing the dynamics of (compartmental) endemic epidemic systems. Using the standard form of a SIR model, a necessary and sufficient condition is formulated for the componentwise absolute stability on a given closed and bounded set, which includes the equilibrium point of the system. It is shown that the class of approachable sets can be considerably enlarged, by applying adequate bijective transformations of the original coordinates, used for the initial statement of the problem. A detailed example illustrates the whole procedure for the exploration of the componentwise absolute stability on a set resulting from a nonsingular linear transformation applied to the original state variables.
- References
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- Published
- 2002-12-31
- Issue
- Vol. 4 No. 4 (2002)
- Section
- Articles