Abstract
In this paper, a Non Standard Finite Difference (NSFD) scheme is constructed, which can be used to determine numerical solutions for an epidemic model with vaccination. Here the NSFD method is employed to derive a set of difference equations for the epidemic model with vaccination. We show that difference equations have the same dynamics as the original differential system, such as the positivity of the solutions and the stability of the equilibria, without being restricted by the time step. Our proof of global stability utilizes the method of Lyapunov functions. Numerical simulation illustrates the effectiveness of our results.
| Original language | English |
|---|---|
| Pages (from-to) | 635-646 |
| Number of pages | 12 |
| Journal | International Journal of Applied Mathematics and Computer Science |
| Volume | 24 |
| Issue number | 3 |
| DOIs | |
| State | Published - 1 Sep 2014 |
| Externally published | Yes |
UN SDGs
This output contributes to the following UN Sustainable Development Goals (SDGs)
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SDG 3 Good Health and Well-being
Keywords
- Lyapunov function
- nonstandard finite differences
- stability
- unconditional positivity
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