Mathematical Modeling of the Transmission Dynamics of Syphilis Disease Using Differential Transformation Method

Mbachu Hope Ifeyinwa

doi:doi:10.11648/j.mma.20200502.11

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Mathematical Modeling of the Transmission Dynamics of Syphilis Disease Using Differential Transformation Method

Mbachu Hope Ifeyinwa

Published in Mathematical Modelling and Applications (Volume 5, Issue 2)

Received: 21 February 2020 Accepted: 9 March 2020 Published: 24 March 2020

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Abstract

In this work, we developed a mathematical model for the transmission dynamics of the Syphilis disease under some assumptions made. The method of differential transformation is employed to compute an approximation to the solution of the non-linear systems of differential equations for the transmission dynamic of the disease model. The differential transformation method is a semi-analytic numerical method or technique, which depends on Taylor series and has application in many areas including Biomathematics. The disease-free equilibrium of the syphilis model is analyzed for local asymptotic stability and the associated epidemic basic reproduction number R₀ is less than unity. It is also known that the global dynamics of the disease are completely determined by the basic reproduction number. Sensitivity analysis is performed on the model’s parameters to investigate the most sensitive parameters in the dynamics of the disease, for control and eradication.

Published in	Mathematical Modelling and Applications (Volume 5, Issue 2)
DOI	10.11648/j.mma.20200502.11
Page(s)	47-54
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2020. Published by Science Publishing Group

Keywords

Syphilis Disease, Differential Transformation Method, Transmission Dynamics, Endemic Equillibrium, Mathematical Modeling

References

[1]	Akinboro F. S., Alao S. and Akinpelu F. O. (2014) Numerical Solution of SIR Model using Differential Transformation Method and Variational Iteration Method. Vol. 22. Pg 82-92.
[2]	Aris S. and Ivey R. M. S. (2004) Principles of Mathematical Modeling; 1st Edition, Academic Press, New York.
[3]	Brauer F. and Castillo-Chavez C. (2001) Mathematical Models in Population Biology and Epidemiology the Amerian Mathematical Monthly 40: 267-291.
[4]	Dym C. L. and Ivey E. S. (2002) Principles of Mathematical Modeling, 1st Edition, Academic Press, New York.
[5]	Garnett G. P., Aral S. O., Hoyle D. V., Cates W. and Anderson R. M. (1997) The natural history of syphilis: implications for the transition dynamics and control of infection. Sex Transm Dis. Vol. IV. Pp 185-200.
[6]	Gumel A. B., Jean M. S., Oluwaseun S., Yibeltal A. T. (2017). Mathematics of a sex-structured model for syphilis transmission dynamics.
[7]	Iboi E. and Okuonghae D. (2016) Population Dynamics of a Mathematical model for syphilis. Appl Math Modeling, Vol. IV, Pp. 3573-3590.
[8]	Kermack, W. O and McKendrick, A. G (1927). A Contribution to the Mathematical Theory of Epidemics, Proceedings of the Royal Society Vol. 115, No. 772, pp. 700-721.
[9]	Kiarie J., Mishra C. K., Temmerman M. and Newman L. (2015) Accelerating the dual elimination of mother-to-child transmission of syphilis and HIV: why now?, International Journal of Gynecology Obstetrics; Vol. I, Pp. 130.
[10]	World Bank Life expectancy at birth data.worldbank.org; Accessed 12 May 2018.
[11]	World Health Report, the world health report 2004-changing history. http://www.who.int/whr/2004/en/, Assessed June 28, 2018.

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APA Style

Mbachu Hope Ifeyinwa. (2020). Mathematical Modeling of the Transmission Dynamics of Syphilis Disease Using Differential Transformation Method. Mathematical Modelling and Applications, 5(2), 47-54. https://doi.org/10.11648/j.mma.20200502.11

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ACS Style

Mbachu Hope Ifeyinwa. Mathematical Modeling of the Transmission Dynamics of Syphilis Disease Using Differential Transformation Method. Math. Model. Appl. 2020, 5(2), 47-54. doi: 10.11648/j.mma.20200502.11

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AMA Style

Mbachu Hope Ifeyinwa. Mathematical Modeling of the Transmission Dynamics of Syphilis Disease Using Differential Transformation Method. Math Model Appl. 2020;5(2):47-54. doi: 10.11648/j.mma.20200502.11

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@article{10.11648/j.mma.20200502.11,
  author = {Mbachu Hope Ifeyinwa},
  title = {Mathematical Modeling of the Transmission Dynamics of Syphilis Disease Using Differential Transformation Method},
  journal = {Mathematical Modelling and Applications},
  volume = {5},
  number = {2},
  pages = {47-54},
  doi = {10.11648/j.mma.20200502.11},
  url = {https://doi.org/10.11648/j.mma.20200502.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20200502.11},
  abstract = {In this work, we developed a mathematical model for the transmission dynamics of the Syphilis disease under some assumptions made. The method of differential transformation is employed to compute an approximation to the solution of the non-linear systems of differential equations for the transmission dynamic of the disease model. The differential transformation method is a semi-analytic numerical method or technique, which depends on Taylor series and has application in many areas including Biomathematics. The disease-free equilibrium of the syphilis model is analyzed for local asymptotic stability and the associated epidemic basic reproduction number R0 is less than unity. It is also known that the global dynamics of the disease are completely determined by the basic reproduction number. Sensitivity analysis is performed on the model’s parameters to investigate the most sensitive parameters in the dynamics of the disease, for control and eradication.},
 year = {2020}
}

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TY  - JOUR
T1  - Mathematical Modeling of the Transmission Dynamics of Syphilis Disease Using Differential Transformation Method
AU  - Mbachu Hope Ifeyinwa
Y1  - 2020/03/24
PY  - 2020
N1  - https://doi.org/10.11648/j.mma.20200502.11
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AB  - In this work, we developed a mathematical model for the transmission dynamics of the Syphilis disease under some assumptions made. The method of differential transformation is employed to compute an approximation to the solution of the non-linear systems of differential equations for the transmission dynamic of the disease model. The differential transformation method is a semi-analytic numerical method or technique, which depends on Taylor series and has application in many areas including Biomathematics. The disease-free equilibrium of the syphilis model is analyzed for local asymptotic stability and the associated epidemic basic reproduction number R0 is less than unity. It is also known that the global dynamics of the disease are completely determined by the basic reproduction number. Sensitivity analysis is performed on the model’s parameters to investigate the most sensitive parameters in the dynamics of the disease, for control and eradication.
VL  - 5
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ER  -

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Author Information

Mbachu Hope Ifeyinwa

Department of Statistics, Imo State University, Owerri, Nigeria

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APA Style

Mbachu Hope Ifeyinwa. (2020). Mathematical Modeling of the Transmission Dynamics of Syphilis Disease Using Differential Transformation Method. Mathematical Modelling and Applications, 5(2), 47-54. https://doi.org/10.11648/j.mma.20200502.11

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ACS Style

Mbachu Hope Ifeyinwa. Mathematical Modeling of the Transmission Dynamics of Syphilis Disease Using Differential Transformation Method. Math. Model. Appl. 2020, 5(2), 47-54. doi: 10.11648/j.mma.20200502.11

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AMA Style

Mbachu Hope Ifeyinwa. Mathematical Modeling of the Transmission Dynamics of Syphilis Disease Using Differential Transformation Method. Math Model Appl. 2020;5(2):47-54. doi: 10.11648/j.mma.20200502.11

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@article{10.11648/j.mma.20200502.11,
  author = {Mbachu Hope Ifeyinwa},
  title = {Mathematical Modeling of the Transmission Dynamics of Syphilis Disease Using Differential Transformation Method},
  journal = {Mathematical Modelling and Applications},
  volume = {5},
  number = {2},
  pages = {47-54},
  doi = {10.11648/j.mma.20200502.11},
  url = {https://doi.org/10.11648/j.mma.20200502.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20200502.11},
  abstract = {In this work, we developed a mathematical model for the transmission dynamics of the Syphilis disease under some assumptions made. The method of differential transformation is employed to compute an approximation to the solution of the non-linear systems of differential equations for the transmission dynamic of the disease model. The differential transformation method is a semi-analytic numerical method or technique, which depends on Taylor series and has application in many areas including Biomathematics. The disease-free equilibrium of the syphilis model is analyzed for local asymptotic stability and the associated epidemic basic reproduction number R0 is less than unity. It is also known that the global dynamics of the disease are completely determined by the basic reproduction number. Sensitivity analysis is performed on the model’s parameters to investigate the most sensitive parameters in the dynamics of the disease, for control and eradication.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Mathematical Modeling of the Transmission Dynamics of Syphilis Disease Using Differential Transformation Method
AU  - Mbachu Hope Ifeyinwa
Y1  - 2020/03/24
PY  - 2020
N1  - https://doi.org/10.11648/j.mma.20200502.11
DO  - 10.11648/j.mma.20200502.11
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 47
EP  - 54
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20200502.11
AB  - In this work, we developed a mathematical model for the transmission dynamics of the Syphilis disease under some assumptions made. The method of differential transformation is employed to compute an approximation to the solution of the non-linear systems of differential equations for the transmission dynamic of the disease model. The differential transformation method is a semi-analytic numerical method or technique, which depends on Taylor series and has application in many areas including Biomathematics. The disease-free equilibrium of the syphilis model is analyzed for local asymptotic stability and the associated epidemic basic reproduction number R0 is less than unity. It is also known that the global dynamics of the disease are completely determined by the basic reproduction number. Sensitivity analysis is performed on the model’s parameters to investigate the most sensitive parameters in the dynamics of the disease, for control and eradication.
VL  - 5
IS  - 2
ER  -

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