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Mathematics of a model for Zika transmission dynamics

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Abstract

Zika is a flavivirus transmitted to humans through either the bite of infected Aedes mosquitoes or sexual intercourse with infected individuals. In this paper, we present a mathematical model based on these two modes of transmission. Using the next-generation matrix method, a threshold parameter called basic reproduction number is determined. Sensitivity analysis of the basic reproduction number in terms of parameters involved in its formulation is discussed. A dynamically consistent nonstandard finite difference scheme is designed to replicate the properties of the continuous model. Numerical simulations of the nonstandard finite difference scheme that we have constructed show the number of infected humans due to sexual intercourse with Zika virus infectious individuals. The numerical simulations also support the theoretical analysis of the model.

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Acknowledgements

The authors acknowledge the financial support of the DST/NRF SARChI Chair in Mathematical Models and Methods in Bioengineering and Biosciences from the University of Pretoria and University of South Africa. The authors are grateful to the anonymous reviewers, and the Handling Editor, for their suggestions that have greatly improved the paper.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Limpopo, Mankweng, South Africa

    Y. A. Terefe

  2. Department of Biological Sciences, Old Dominion University, Norfolk, USA

    H. Gaff

  3. Department of Mathematics, University of Namibia, Windhoek, Namibia

    M. Kamga

  4. Department of Conservation Ecology and Entomology, University of Stellenbosch, Stellenbosch, South Africa

    L. van der Mescht

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  1. Y. A. Terefe
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  2. H. Gaff
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  3. M. Kamga
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  4. L. van der Mescht
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Correspondence to Y. A. Terefe.

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Terefe, Y.A., Gaff, H., Kamga, M. et al. Mathematics of a model for Zika transmission dynamics. Theory Biosci. 137, 209–218 (2018). https://doi.org/10.1007/s12064-018-0272-7

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  • DOI: https://doi.org/10.1007/s12064-018-0272-7

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