Periodic solutions: a robust numerical method for an S-I-R model of epidemics |
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| Authors: | F A Milner A Pugliese |
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| Institution: | (1) Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA. milner@math.purdue.edu, US;(2) Department of Mathematics, University of Trento, 38050 Povo (TN), Italy, IT |
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| Abstract: | We describe and analyze a numerical method for an S-I-R type epidemic model. We prove that it is unconditionally convergent
and that solutions it produces share many qualitative and quantitative properties of the solution of the differential problem
being approximated. Finally, we establish explicit sufficient conditions for the unique endemic steady state of the system
to be unstable and we use our numerical algorithm to approximate the solution in such cases and discover that it can be periodic,
just as suggested by the instability of the endemic steady state.
Received: 1 September 1995 / Revised version: 30 April 1997 |
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| Keywords: | : Numerical methods Periodic solutions Instability of equilibrium Epidemic model |
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