A non-standard finite difference scheme for an epidemic model with vaccination

Abstract

The aim of this paper is to construct a non-standard finite difference (NSFD) scheme that can be used to calculate 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 when , the discretized model preserves positivity and global dynamics of the continuous model. Numerical simulation illustrates the effectiveness of our results.

Keywords:

• non-standard difference
• numerical discretized model
• stability
• Lyapunov function

Keywords:

• 03H05
• 34D23

Acknowledgements

The authors thank the anonymous reviewers for their valuable comments and suggestions regarding the presentation of this paper. This work was supported by the National Natural Science Foundation of China (No. 11026189) and the NNSF of Shandong Province (No. ZR2010AQ021).