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Afrika Matematika

, Volume 29, Issue 1–2, pp 277–294 | Cite as

Dynamical analysis and consistent numerics for a delay model of viral infection in phytoplankton population

Article
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Abstract

In this article, the effects of time delay and carrying capacity in the dynamics of viral phytoplankton and consistence numerics are studied. Basic properties and stabilities of equilibria are rigorously analyzed and conditions for stability switches are found. A dynamically consistent nonstandard finite difference scheme for the continuous delay model is designed to verify the results and reveal some interesting features of the model. Some ecological implications and interpretations are provided.

Keywords

Phytoplankton Delay Stability switches Nonstandard finite difference scheme 

Mathematics Subject Classification

37N25 

Notes

Acknowledgements

The author acknowledges the financial supports of South African DST/NRF SARChI chair on Mathematical Models and Methods in Bioengineering and Biosciences \((M^3B^2)\), Department of Mathematics and Applied Mathematics, University of Pretoria and MacArthur Foundation, Bayero University, Kano, Nigeria. The support of the DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) towards this research is hereby acknowledged. Opinions expressed and conclusions arrived at, are those of the author and are not necessarily to be attributed to CoE. Furthermore, the author is grateful to the handling Editor, Chief Editor and the Reviewers.

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Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematical Sciences, Faculty of Physical SciencesBayero UniversityKanoNigeria
  2. 2.Department of Mathematics and Applied MathematicsUniversity of PretoriaPretoriaSouth Africa

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