On Existence and Uniqueness of Syphilis Model

Abdullahi A. A.; Oyeniyi R. B.; Akintunde M. A.

doi:doi:10.11648/j.mma.20160102.14

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On Existence and Uniqueness of Syphilis Model

Abdullahi A. A., Oyeniyi R. B., Akintunde M. A.

Published in Mathematical Modelling and Applications (Volume 1, Issue 2)

Received: 8 September 2016 Accepted: 19 December 2016 Published: 12 January 2017

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Abstract

A good understanding of the transmission dynamics of disease is necessary to proffer solution(s) to syphilis problem. The aim of this research was to use mathematical modelling to understand the intricacies and different approaches to Syphilis screening on epidemic dynamics and the health of MSM. A non-linear mathematical model for the transmission dynamics of syphilis in an heterogeneous setting with complications is developed and analysed. The existence and uniqueness of the system of equations is examined. We use the concept of Lipchitz criteria to analyse the model.

Published in	Mathematical Modelling and Applications (Volume 1, Issue 2)
DOI	10.11648/j.mma.20160102.14
Page(s)	55-58
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), 2017. Published by Science Publishing Group

Keywords

Syphilis, Existence, Lipchitz, Uniqueness

References

[1]	Gilson, R. and Mindel, A. (2001). Infectious and communicable diseases and mode of transmission. British Medical Journal, 322.
[2]	World Health Organization (WHO) (2001). WHO website: http:// www. Who. Int / publishers / en. Html. Geneva.
[3]	Usanga, V. U., Abia, B. L., Efoh I. E, Udoh, P. C., Archibong, E., and Ani, F. (2010). Incidence of gonorrhoea among pregnant among pregnant woman in calabar, Nigeria. The International of Gynaecology and Obstetrics.
[4]	Coffin, L. S.; Newberry, A; Hagan, H; Cleland, C. M; Des Jarlais, D. C; Perlman, D. C, (January 2010). “Syphilis in Drug users in low and middle Income countries’’. The Interantional Journal on drug policy 21 (1): 20–7.
[5]	Gao, L,; Zhang, L; Jin Q ( September 2009). ‘’ Meta-analysis; prevalence of HIV infection and syphilis among MSM in China’’. Sexually transmitted infections 85 (5): 354-8.
[6]	Karp, G; Schlaeffer, F; Jotkowitz, A; Riesenberg, K (January 2009). “Syphilis and Co-infection’’. European journal of internal medicine 20(1): 9-13.
[7]	Yorke, J, A, and Hethcote, H. W (1973). Dynamics and control of the transmission of gonorrhoea.
[8]	Yorke, J, A, and Hethcote, H. W (1984). Gonorrhea transmission dynamics and control. Biometerical Journal, 28.
[9]	World Health Organization (WHO) (2006). Who. technical report series no 810. Geneva.
[10]	Milner, F. A. and Zhao, R. (2010). A new mathematical model of syphilis. Arizonal State University.
[11]	Derrick, N. and Grossman, S. (1976). Differential Equations with Applications. Addison Wesley Publishing Company, Inc Philippines.
[12]	Milner, F. A. and Zhao, R. (2010). A new mathematical model of Syphilis.
[13]	Ashleigh, T. (2015). Using Mathematical models to inform syphilis control strategies in men who have sex with men. Ph. D thesis, Institute of Medical science university of Toronto, Canada.

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APA Style

Abdullahi A. A., Oyeniyi R. B., Akintunde M. A. (2017). On Existence and Uniqueness of Syphilis Model. Mathematical Modelling and Applications, 1(2), 55-58. https://doi.org/10.11648/j.mma.20160102.14

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ACS Style

Abdullahi A. A.; Oyeniyi R. B.; Akintunde M. A. On Existence and Uniqueness of Syphilis Model. Math. Model. Appl. 2017, 1(2), 55-58. doi: 10.11648/j.mma.20160102.14

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AMA Style

Abdullahi A. A., Oyeniyi R. B., Akintunde M. A. On Existence and Uniqueness of Syphilis Model. Math Model Appl. 2017;1(2):55-58. doi: 10.11648/j.mma.20160102.14

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@article{10.11648/j.mma.20160102.14,
  author = {Abdullahi A. A. and Oyeniyi R. B. and Akintunde M. A.},
  title = {On Existence and Uniqueness of Syphilis Model},
  journal = {Mathematical Modelling and Applications},
  volume = {1},
  number = {2},
  pages = {55-58},
  doi = {10.11648/j.mma.20160102.14},
  url = {https://doi.org/10.11648/j.mma.20160102.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20160102.14},
  abstract = {A good understanding of the transmission dynamics of disease is necessary to proffer solution(s) to syphilis problem. The aim of this research was to use mathematical modelling to understand the intricacies and different approaches to Syphilis screening on epidemic dynamics and the health of MSM. A non-linear mathematical model for the transmission dynamics of syphilis in an heterogeneous setting with complications is developed and analysed. The existence and uniqueness of the system of equations is examined. We use the concept of Lipchitz criteria to analyse the model.},
 year = {2017}
}

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TY  - JOUR
T1  - On Existence and Uniqueness of Syphilis Model
AU  - Abdullahi A. A.
AU  - Oyeniyi R. B.
AU  - Akintunde M. A.
Y1  - 2017/01/12
PY  - 2017
N1  - https://doi.org/10.11648/j.mma.20160102.14
DO  - 10.11648/j.mma.20160102.14
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 55
EP  - 58
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20160102.14
AB  - A good understanding of the transmission dynamics of disease is necessary to proffer solution(s) to syphilis problem. The aim of this research was to use mathematical modelling to understand the intricacies and different approaches to Syphilis screening on epidemic dynamics and the health of MSM. A non-linear mathematical model for the transmission dynamics of syphilis in an heterogeneous setting with complications is developed and analysed. The existence and uniqueness of the system of equations is examined. We use the concept of Lipchitz criteria to analyse the model.
VL  - 1
IS  - 2
ER  -

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Author Information

Abdullahi A. A.

Department of Mathematics and Statistics, The Federal Polytechnic, Ado-Ekiti, Nigeria
Oyeniyi R. B.

Department of Mathematics and Statistics, The Federal Polytechnic, Ado-Ekiti, Nigeria
Akintunde M. A.

Department of Statistics, The Federal Polytechnic, Ede, Nigeria

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APA Style

Abdullahi A. A., Oyeniyi R. B., Akintunde M. A. (2017). On Existence and Uniqueness of Syphilis Model. Mathematical Modelling and Applications, 1(2), 55-58. https://doi.org/10.11648/j.mma.20160102.14

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ACS Style

Abdullahi A. A.; Oyeniyi R. B.; Akintunde M. A. On Existence and Uniqueness of Syphilis Model. Math. Model. Appl. 2017, 1(2), 55-58. doi: 10.11648/j.mma.20160102.14

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AMA Style

Abdullahi A. A., Oyeniyi R. B., Akintunde M. A. On Existence and Uniqueness of Syphilis Model. Math Model Appl. 2017;1(2):55-58. doi: 10.11648/j.mma.20160102.14

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@article{10.11648/j.mma.20160102.14,
  author = {Abdullahi A. A. and Oyeniyi R. B. and Akintunde M. A.},
  title = {On Existence and Uniqueness of Syphilis Model},
  journal = {Mathematical Modelling and Applications},
  volume = {1},
  number = {2},
  pages = {55-58},
  doi = {10.11648/j.mma.20160102.14},
  url = {https://doi.org/10.11648/j.mma.20160102.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20160102.14},
  abstract = {A good understanding of the transmission dynamics of disease is necessary to proffer solution(s) to syphilis problem. The aim of this research was to use mathematical modelling to understand the intricacies and different approaches to Syphilis screening on epidemic dynamics and the health of MSM. A non-linear mathematical model for the transmission dynamics of syphilis in an heterogeneous setting with complications is developed and analysed. The existence and uniqueness of the system of equations is examined. We use the concept of Lipchitz criteria to analyse the model.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - On Existence and Uniqueness of Syphilis Model
AU  - Abdullahi A. A.
AU  - Oyeniyi R. B.
AU  - Akintunde M. A.
Y1  - 2017/01/12
PY  - 2017
N1  - https://doi.org/10.11648/j.mma.20160102.14
DO  - 10.11648/j.mma.20160102.14
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 55
EP  - 58
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20160102.14
AB  - A good understanding of the transmission dynamics of disease is necessary to proffer solution(s) to syphilis problem. The aim of this research was to use mathematical modelling to understand the intricacies and different approaches to Syphilis screening on epidemic dynamics and the health of MSM. A non-linear mathematical model for the transmission dynamics of syphilis in an heterogeneous setting with complications is developed and analysed. The existence and uniqueness of the system of equations is examined. We use the concept of Lipchitz criteria to analyse the model.
VL  - 1
IS  - 2
ER  -

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