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Periodic solutions: A robust numerical method for an S-I-R model of epidemics. (English) Zbl 0945.92017
Summary: 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.

MSC:
92D30 Epidemiology
65R20 Numerical methods for integral equations
45K05 Integro-partial differential equations
45M10 Stability theory for integral equations
45M15 Periodic solutions of integral equations
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