Related Experiment Video
Updated: Aug 11, 2026

Estimating Virus Production Rates in Aquatic Systems
Published on: September 22, 2010
Periodic solutions: a robust numerical method for an S-I-R model of epidemics
1Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA. milner@math.purdue.edu
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.
Related Concept Videos
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Steps in Outbreak Investigation
Parametric Survival Analysis: Weibull and Exponential Methods
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
Exponential Equations with Logarithms: Problem Solving
Exponential Equations for Modeling Growth
Modeling with Differential Equations

