title: Periodic solutions: a robust numerical method for an S-I-R model of epidemics.
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.
authors.affiliation: Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA. milner@math.purdue.edu
authors.forename: F A
authors.initials: FA
authors.lastname: Milner
authors.forename: A
authors.initials: A
authors.lastname: Pugliese
mesh_terms: D000163:Acquired Immunodeficiency Syndrome / Q000453:epidemiology; D000465:Algorithms; D004196:Disease Outbreaks / Q000706:statistics & numerical data*; D015658:HIV Infections / Q000453:epidemiology; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D010507:Periodicity