| Peer-Reviewed

Modeling the Epidemiology of Malaria and Control with Estimate of the Basic Repro-duction Number

Published: 20 February 2013
Views:       Downloads:
Abstract

Strategies for controlling the epidemiology of many infectious diseases such as malaria include a rapid reduc-tion in both the infected and susceptible population via treatment and vaccination. In this paper, we have modified the Tumwiine et al. (2007) mathematical model for the transmission of malaria by including a vaccination parameter. We have shown that the model has a unique disease-free equilibrium state which is locally and globally asymptotically stable, if 1, and that the endemic equilibrium exist provided > 1, where is a parameter which depends on the given model parameters. Numerical simulations of the modified model clearly show that, with a proper combination of treatment and vaccination, offered at about 65% each on the susceptible and infected population, malaria can be eradicated from the community.

Published in Pure and Applied Mathematics Journal (Volume 2, Issue 1)
DOI 10.11648/j.pamj.20130201.17
Page(s) 42-50
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), 2013. Published by Science Publishing Group

Keywords

Malaria, Disease-Free Equilibrium Point, Reproduction Number, Endemic Equilibrium Point, Global Asymp-totical Stability, Lyaponuv Function

References
[1] Aslan G, Seyrek A. (2007). The diagnosis of malaria and identification of plasmodium species by polymerase chain reaction in turkey. pp:87-102
[2] Deressa, Wakgari, Ali, Ahmed and Berhane, (2000). Yemane Maternal responses to childhood febrile illnesses in an area of seasonal malaria transmission in rural ethiopia. Acta tropica, pp: 134-166
[3] Dietz, Molineaux and Thomas (1974) Development of a new version of the Liverpool malaria model. Oxford University Press, Oxford.
[4] Kakkilaya, B. S. (2003). Rapid diagnosis of malaria, lab medicine, 8(34), 602-608
[5] Nedelman J. (1985) Estimation for a model of multiple malaria infections. Phil. Trans. R. Soc. London. 65(4), 291: 451-524
[6] Perandin F. (2003). Development of a Real-time PCR assay for detection of plasmodium falciparum, plsmodium vivax, and plasmodium ovale for routine clinical diagnosis. Journal of clinical microbiology, 42 (3), 1214-1219, A Moody, Rapid diagnostic tests for malaria parasites, Clin Microbiol Rev 15 (2002), pp. 66–78.
[7] Tumwiine, Mugisha J. Y. T and Lubobi L. S (2007). Applied mathematics and computation. 189(2007) pp1953-1965.
[8] Yang Hyun. M, (2000) Mapping and predicting malaria transmission in the People’s Republic of China, using intergrated biology-driven and statistical models. Phil. Trans. R. Soc. London, pp: 291: 451-524.
Cite This Article
  • APA Style

    Adamu Abdul Kareem, Anande Richard Kimbir. (2013). Modeling the Epidemiology of Malaria and Control with Estimate of the Basic Repro-duction Number. Pure and Applied Mathematics Journal, 2(1), 42-50. https://doi.org/10.11648/j.pamj.20130201.17

    Copy | Download

    ACS Style

    Adamu Abdul Kareem; Anande Richard Kimbir. Modeling the Epidemiology of Malaria and Control with Estimate of the Basic Repro-duction Number. Pure Appl. Math. J. 2013, 2(1), 42-50. doi: 10.11648/j.pamj.20130201.17

    Copy | Download

    AMA Style

    Adamu Abdul Kareem, Anande Richard Kimbir. Modeling the Epidemiology of Malaria and Control with Estimate of the Basic Repro-duction Number. Pure Appl Math J. 2013;2(1):42-50. doi: 10.11648/j.pamj.20130201.17

    Copy | Download

  • @article{10.11648/j.pamj.20130201.17,
      author = {Adamu Abdul Kareem and Anande Richard Kimbir},
      title = {Modeling the Epidemiology of Malaria and Control with Estimate of the Basic Repro-duction Number},
      journal = {Pure and Applied Mathematics Journal},
      volume = {2},
      number = {1},
      pages = {42-50},
      doi = {10.11648/j.pamj.20130201.17},
      url = {https://doi.org/10.11648/j.pamj.20130201.17},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130201.17},
      abstract = {Strategies for controlling the epidemiology of many infectious diseases such as malaria include a rapid reduc-tion in both the infected and susceptible population via treatment and vaccination. In this paper, we have modified the Tumwiine et al. (2007) mathematical model for the transmission of malaria by including a vaccination parameter. We have shown that the model has a unique disease-free equilibrium state which is locally and globally asymptotically stable, if    1, and that the endemic equilibrium exist provided   > 1, where  is a parameter which depends on the given model parameters. Numerical simulations of the modified model clearly show that, with a proper combination of treatment and vaccination, offered at about 65% each on the susceptible and infected population, malaria can be eradicated from the community.},
     year = {2013}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Modeling the Epidemiology of Malaria and Control with Estimate of the Basic Repro-duction Number
    AU  - Adamu Abdul Kareem
    AU  - Anande Richard Kimbir
    Y1  - 2013/02/20
    PY  - 2013
    N1  - https://doi.org/10.11648/j.pamj.20130201.17
    DO  - 10.11648/j.pamj.20130201.17
    T2  - Pure and Applied Mathematics Journal
    JF  - Pure and Applied Mathematics Journal
    JO  - Pure and Applied Mathematics Journal
    SP  - 42
    EP  - 50
    PB  - Science Publishing Group
    SN  - 2326-9812
    UR  - https://doi.org/10.11648/j.pamj.20130201.17
    AB  - Strategies for controlling the epidemiology of many infectious diseases such as malaria include a rapid reduc-tion in both the infected and susceptible population via treatment and vaccination. In this paper, we have modified the Tumwiine et al. (2007) mathematical model for the transmission of malaria by including a vaccination parameter. We have shown that the model has a unique disease-free equilibrium state which is locally and globally asymptotically stable, if    1, and that the endemic equilibrium exist provided   > 1, where  is a parameter which depends on the given model parameters. Numerical simulations of the modified model clearly show that, with a proper combination of treatment and vaccination, offered at about 65% each on the susceptible and infected population, malaria can be eradicated from the community.
    VL  - 2
    IS  - 1
    ER  - 

    Copy | Download

Author Information
  • Mathematical Sciences Department, School of Pure & Applied Sciences, Modibbo Adama University of Technology, Yola, Adamawa State, Nigeria

  • Department of Mathematics & Computer, University of Agriculture, Markudi, Benue State, Nigeria

  • Sections