Time-Scale Analysis of Malaria Dynamics in Human-Mosquito Population

Kodwo Annan

doi:doi:10.11648/j.ijtam.20170302.17

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Time-Scale Analysis of Malaria Dynamics in Human-Mosquito Population

Kodwo Annan

Published in International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 2)

Received: 20 January 2017 Accepted: 13 February 2017 Published: 2 March 2017

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Abstract

More realistic human-mosquito population mathematical model in which re-infected asymptomatic humans are considered is presented. Six possible time-scale of events for model transition from non-endemic to endemic state are analyzed. Results show that the buildup of the latent asymptomatic humans at steady state is the main dynamics of malaria in the endemic region. This become evident in the time scale of about 1-2 weeks and thus influences the mode of infection in the malaria transmission analysis.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 2)
DOI	10.11648/j.ijtam.20170302.17
Page(s)	88-93
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), 2024. Published by Science Publishing Group

Keywords

Malaria Transmission, Timescale Analysis, Mathematical Modeling

References

[1]	J. D. Charlwood, T. Smith, P. F. Billingsley, W. Takken, E. Lyimo and J. Meuwissen, Survival and infection probabilities of anthropophagic anophelines from an area of high prevalence of Plasmodium falciparum in humans, Bull. Entomol. Res., 87 (1997): pp. 445-453.
[2]	K. Annan and C. Mukinay. Stability and Time-Scale Analysis of Malaria Transmission in Human-Mosquito Population, International Journal of Systems Science and Applied Mathematics. Vol. 2, No. 1, 2017, pp. 1-9. doi: 10.11648/j.ijssam.20170201.11.
[3]	K. A. Cullen, and Paul M Arguin. "Malaria Surveillance--United States, 2012." Morbidity and Mortality Weekly Report. Surveillance Summaries (Washington, D. C.: 2002) 63.12 (2014): 1-22. MEDLINE with Full Text. Web. 6 Sept. 2015.
[4]	M. Dako-Gyeke and H. M. Kofie. "Factors Influencing Prevention and Control of Malaria among Pregnant Women Resident in Urban Slums, Southern Ghana." African Journal of Reproductive Health 19.1 (2015): 44-53. MEDLINE with Full Text. Web. 7 Sept. 2015.
[5]	S. Olaniyi, O. S. Obabiyi. Mathematical Model for Malaria Transmission Dynamics in Human and Mosquito Populations with Nonlinear Forces of Infection. IJPAM Vol. 88 No. 1, 2013, 125-156
[6]	H. F. Huo, G. M. Qiu. Stability of a Mathematical Model of Malaria Transmission with Relapse. Abs. & Applied Analysis, Volume 2014.
[7]	C. Chiyaka, W. Garira, S. Dube. Transmission Model of Endemic Human Malaria in a Partially Immune Population. Math & Comp. Modelling 46 (2007) 806-822.
[8]	WHO, World Malaria Report 2016. Geneva: World Health Organization; 2016. Licence: CC BY-NC-SA 3.0 IGO.
[9]	P. Brown, Trials and tribulations of a malaria vaccine, New Scientist (1991) 18-19.
[10]	H. M. Yang, Malaria transmission model for different levels of acquired immunity and temperature dependent parameters (vector). J. Public Health, 34 (2000), 223-231.
[11]	B. Ogutu, A. B. Tiono, M. Makanga, Z. Premji, A. D. Gbado, D. Ubben, A. C. Marrast, O. Gaye. Treatment of asymptomatic carriers with artemether-lumefantrine: an opportunity to reduce the burden of malaria. Malaria Journal, [online]. [viewed 09/11/2016].
[12]	M. Imwong, K. Stepniewska, R. Tripura, et al. Numerical Distributions of Parasite Densities during Asymptomatic Malaria. JID (2016) 213, 1322-1329.
[13]	J. Tumwiine, J. Mugisha, L. Luboobi. A mathematical model for the dynamics of malaria in a human host and mosquito vector with temporary immunity. Journal of Applied Math. & Computation, Vol. 189 (2005), 1953-1965.
[14]	N. Bacaer and C. Sokhna. A reaction-diffusion system modeling the spread of resistance to an antimalarial drug. Math. Biosci. Engrg, Vol. 2 pp. 227-238, 2005.
[15]	J. Li, Y. Zhao, S. Li. Fast and slow dynamics of malaria model with relapse. Mathematical Biosci., Vol. 246, No. 1, pp. 94-104, 2013.

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Kodwo Annan. (2017). Time-Scale Analysis of Malaria Dynamics in Human-Mosquito Population. International Journal of Theoretical and Applied Mathematics, 3(2), 88-93. https://doi.org/10.11648/j.ijtam.20170302.17

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ACS Style

Kodwo Annan. Time-Scale Analysis of Malaria Dynamics in Human-Mosquito Population. Int. J. Theor. Appl. Math. 2017, 3(2), 88-93. doi: 10.11648/j.ijtam.20170302.17

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AMA Style

Kodwo Annan. Time-Scale Analysis of Malaria Dynamics in Human-Mosquito Population. Int J Theor Appl Math. 2017;3(2):88-93. doi: 10.11648/j.ijtam.20170302.17

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@article{10.11648/j.ijtam.20170302.17,
  author = {Kodwo Annan},
  title = {Time-Scale Analysis of Malaria Dynamics in Human-Mosquito Population},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {3},
  number = {2},
  pages = {88-93},
  doi = {10.11648/j.ijtam.20170302.17},
  url = {https://doi.org/10.11648/j.ijtam.20170302.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170302.17},
  abstract = {More realistic human-mosquito population mathematical model in which re-infected asymptomatic humans are considered is presented. Six possible time-scale of events for model transition from non-endemic to endemic state are analyzed. Results show that the buildup of the latent asymptomatic humans at steady state is the main dynamics of malaria in the endemic region. This become evident in the time scale of about 1-2 weeks and thus influences the mode of infection in the malaria transmission analysis.},
 year = {2017}
}

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TY  - JOUR
T1  - Time-Scale Analysis of Malaria Dynamics in Human-Mosquito Population
AU  - Kodwo Annan
Y1  - 2017/03/02
PY  - 2017
N1  - https://doi.org/10.11648/j.ijtam.20170302.17
DO  - 10.11648/j.ijtam.20170302.17
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 88
EP  - 93
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20170302.17
AB  - More realistic human-mosquito population mathematical model in which re-infected asymptomatic humans are considered is presented. Six possible time-scale of events for model transition from non-endemic to endemic state are analyzed. Results show that the buildup of the latent asymptomatic humans at steady state is the main dynamics of malaria in the endemic region. This become evident in the time scale of about 1-2 weeks and thus influences the mode of infection in the malaria transmission analysis.
VL  - 3
IS  - 2
ER  -

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Author Information

Kodwo Annan

School of Science & Technology, Georgia Gwinnett College, Lawrenceville, USA

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Kodwo Annan. (2017). Time-Scale Analysis of Malaria Dynamics in Human-Mosquito Population. International Journal of Theoretical and Applied Mathematics, 3(2), 88-93. https://doi.org/10.11648/j.ijtam.20170302.17

Copy | Download

ACS Style

Kodwo Annan. Time-Scale Analysis of Malaria Dynamics in Human-Mosquito Population. Int. J. Theor. Appl. Math. 2017, 3(2), 88-93. doi: 10.11648/j.ijtam.20170302.17

Copy | Download

AMA Style

Kodwo Annan. Time-Scale Analysis of Malaria Dynamics in Human-Mosquito Population. Int J Theor Appl Math. 2017;3(2):88-93. doi: 10.11648/j.ijtam.20170302.17

Copy | Download

@article{10.11648/j.ijtam.20170302.17,
  author = {Kodwo Annan},
  title = {Time-Scale Analysis of Malaria Dynamics in Human-Mosquito Population},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {3},
  number = {2},
  pages = {88-93},
  doi = {10.11648/j.ijtam.20170302.17},
  url = {https://doi.org/10.11648/j.ijtam.20170302.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170302.17},
  abstract = {More realistic human-mosquito population mathematical model in which re-infected asymptomatic humans are considered is presented. Six possible time-scale of events for model transition from non-endemic to endemic state are analyzed. Results show that the buildup of the latent asymptomatic humans at steady state is the main dynamics of malaria in the endemic region. This become evident in the time scale of about 1-2 weeks and thus influences the mode of infection in the malaria transmission analysis.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Time-Scale Analysis of Malaria Dynamics in Human-Mosquito Population
AU  - Kodwo Annan
Y1  - 2017/03/02
PY  - 2017
N1  - https://doi.org/10.11648/j.ijtam.20170302.17
DO  - 10.11648/j.ijtam.20170302.17
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 88
EP  - 93
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20170302.17
AB  - More realistic human-mosquito population mathematical model in which re-infected asymptomatic humans are considered is presented. Six possible time-scale of events for model transition from non-endemic to endemic state are analyzed. Results show that the buildup of the latent asymptomatic humans at steady state is the main dynamics of malaria in the endemic region. This become evident in the time scale of about 1-2 weeks and thus influences the mode of infection in the malaria transmission analysis.
VL  - 3
IS  - 2
ER  -

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