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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 471-492 |
| Number of pages | 22 |
| Journal | Journal Of Mathematical Biology |
| Volume | 39 |
| Issue number | 6 |
| DOIs | |
| State | Published - Dec 1999 |
| Externally published | Yes |
Keywords
- Epidemic model
- Instability of equilibrium
- Numerical methods
- Periodic solutions
ASJC Scopus subject areas
- Modeling and Simulation
- Agricultural and Biological Sciences (miscellaneous)
- Applied Mathematics