Numerical Modeling of SEIR Measles Dynamics with Diffusion

Authors

  • Nauman Ahmed Department of Mathematics,University of Management and Technology, Lahore; Department of Mathematics, University of Lahore, Lahore
  • M. Rafiq Faculty of Electrical Engineering,University of Central Punjab, Lahore
  • M. A. Rehman Department of Mathematics,University of Management and Technology, Lahore
  • Mubasher Ali Department of Electrical Engineering, University of Lahore, Lahore
  • M. O. Ahmad Department of Mathematics, University of Lahore, Lahore

DOI:

https://doi.org/10.26713/cma.v9i3.794

Keywords:

SEIR Measles epidemic model with diffusion, Finite difference scheme, Positivity, Consistency, Stability

Abstract

A novel unconditionally positive finite difference (FD) scheme is developed to solve numerically SEIR measles epidemic model with diffusion. In population dynamics, positivity of subpopulations is an essential requirement. The proposed FD scheme preserves the positivity of the solution of the model. The consistency and unconditional stability is proved. The proposed FD scheme is explicit in nature which is an extra feature of this scheme. Comparisons are also made with forward Euler explicit FD scheme and Crank Nicolson implicit FD scheme. Simulations of a numerical test are also presented to verify all the attributes of the proposed scheme.

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References

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Published

25-09-2018
CITATION

How to Cite

Ahmed, N., Rafiq, M., Rehman, M. A., Ali, M., & Ahmad, M. O. (2018). Numerical Modeling of SEIR Measles Dynamics with Diffusion. Communications in Mathematics and Applications, 9(3), 315–326. https://doi.org/10.26713/cma.v9i3.794

Issue

Vol. 9 No. 3 (2018)

Section

Research Article

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