A control theoretic approach to containing the spread of rabies
UNSPECIFIED. (2001) A control theoretic approach to containing the spread of rabies. IMA JOURNAL OF MATHEMATICS APPLIED IN MEDICINE AND BIOLOGY, 18 (1). pp. 1-23. ISSN 0265-0746Full text not available from this repository.
Many problems in medicine and biology involve some kind of spatial spread, and quite often the need to control it. A large proportion of medical and biological systems distinguish themselves from those found in engineering by the way the control acts. We illustrate this by considering the specific example of the spread of rabies among foxes.
We first give a brief description of a model proposed by Murray et al. (Murray, J. D., Stanley, E. A. & Brown, D. L., Proc. R. Sec. Lend., B 229, 111-150 (1986)), which we extend to include the control mechanism. The problem is to prevent the spread of rabies by vaccinating foxes via the distribution of bait in a region around an observed outbreak.
The extended model can be formulated as a nonlinear time-varying control system described by partial differential equations. In contrast to most engineering type control problems, the control does not continuously affect the system but only acts through the initial distributions. We briefly outline a general theory developed for dealing with such nonlinear systems by the use of a fixed point theorem. The problem and the theory are illustrated by some numerical simulations.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Journal or Publication Title:||IMA JOURNAL OF MATHEMATICS APPLIED IN MEDICINE AND BIOLOGY|
|Publisher:||OXFORD UNIV PRESS|
|Official Date:||March 2001|
|Number of Pages:||23|
|Page Range:||pp. 1-23|
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