Positivity preserving operator splitting nonstandard finite difference methods for SEIR reaction diffusion model

• Main Authors: Ahmed Nauman, S.S. Tahira, Rafiq M., Rehman M.A., Ali Mubasher, Ahmad M.O.
• Format: Article
• Language: English
• Published: De Gruyter 2019-04-01
• Series: Open Mathematics
• Subjects: seir reaction diffusion model; operator splitting techniques; positivity; bifurcation value
• Online Access: https://doi.org/10.1515/math-2019-0027
• ISSN: 2391-5455

In this work, we will introduce two novel positivity preserving operator splitting nonstandard finite difference (NSFD) schemes for the numerical solution of SEIR reaction diffusion epidemic model. In epidemic model of infection diseases, positivity is an important property of the continuous system because negative value of a subpopulation is meaningless. The proposed operator splitting NSFD schemes are dynamically consistent with the solution of the continuous model. First scheme is conditionally stable while second operator splitting scheme is unconditionally stable. The stability of the diffusive SEIR model is also verified numerically with the help of Routh-Hurwitz stability condition. Bifurcation value of transmission coefficient is also carried out with and without diffusion. The proposed operator splitting NSFD schemes are compared with the well-known operator splitting finite difference (FD) schemes.