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

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...

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Bibliographic Details
Published inOpen mathematics (Warsaw, Poland) Vol. 17; no. 1; pp. 313 - 330
Main Authors Ahmed, Nauman, S.S., Tahira, Rafiq, M., Rehman, M.A., Ali, Mubasher, Ahmad, M.O.
Format Journal Article
LanguageEnglish
Published Warsaw De Gruyter 29.04.2019
De Gruyter Poland
Subjects
bifurcation value
Diffusion
Epidemics
Finite difference method
Mathematical analysis
Mathematical models
operator splitting techniques
positivity
SEIR reaction diffusion model
Splitting
Stability
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Summary: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.
ISSN:2391-5455
2391-5455
DOI:10.1515/math-2019-0027