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Mathematical Model of Controlling the Spread of Malaria Disease Using Intervention Strategies

Received: 29 January 2020     Accepted: 9 March 2020     Published: 11 November 2020
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Abstract

This paper proposes and analyses a basic deterministic mathematical model to investigate Simulation for controlling the spread of malaria Diseases Transmission dynamics. The model has seven non-linear differential equations which describe the control of malaria with two state variables for mosquito’s populations and five state variables for human’s population. To represent the classification of human population we have included protection and treatment compartments to the basic SIR epidemic model and extended it to SPITR model and to introduce the new SPITR modified model by adding vaccination for the transmission dynamics of malaria with four time dependent control measures in Ethiopia Insecticide treated bed nets (ITNS), Treatments, Indoor Residual Spray (IRs) and Intermittent preventive treatment of malaria in pregnancy (IPTP). The models are analyzed qualitatively to determine criteria for control of a malaria transmission dynamics and are used to calculate the basic reproduction R0. The equilibria of malaria models are determined. In addition to having a disease-free equilibrium, which is globally asymptotically stable when the R0<1, the basic malaria model manifest one's possession of (a quality of) the phenomenon of backward bifurcation where a stable disease-free equilibrium co-exists (at the same time) with a stable endemic equilibrium for a certain range of associated reproduction number less than one. The results also designing the effects of some model parameters, the infection rate and biting rate. The numerical analysis and numerical simulation results of the model suggested that the most effective strategies for controlling or eradicating the spread of malaria were suggest using insecticide treated bed nets, indoor residual spraying, prompt effective diagnosis and treatment of infected individuals with vaccination is more effective for children.

Published in Pure and Applied Mathematics Journal (Volume 9, Issue 6)
DOI 10.11648/j.pamj.20200906.11
Page(s) 101-108
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

Malaria, Basic Reproduction Number, Backward Bifurcation Analysis, Vaccination and SPITR Modified Model

References
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[2] Nita. H. Shah and Jyoti Gupta (2013),"SEIR Model and Simulation for Vector Borne Diseases", Applied Mathematics Vol. 4, Pp. 13–17.
[3] Samwel Oseko Nyachae, Johana K. Sigey Jeconiah A. Okello, James M. Okwoyo and D. Theuri (2014),"A Study for the Spread of Malaria in Nyamira Town - Kenya, The SIJ Transactions on Computer Science Engineering and its Applications (CSEA), The Standard International Journals (The SIJ), Vol. 2, No. 3 (1), Pp. 53-60.
[4] Rollback Malaria. What is malaria? http://www.rollbackmalaria.pdf. (2010-05-10).
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[6] Bayoh MN, Mathias DK, Odiere MR, Mutuku FM, Kamau L, et al.. (2010) Anopheles gambiae: historical population decline associated with regional distribution of insecticide-treated bed nets in western Nyanza province, Kenya. Malaria Journal 9.
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[10] P. M. M. Mwamtobe (2010), "Modeling the Effects of Multi Intervention Campaigns for the Malaria Epidemic in Malawi", M. Sc. (Mathematical Modeling) Dissertation, University of Dar es Salaam, Tanzania.
[11] G. A. Ngwa, W. S. Shu, A mathematical model for endemic malaria with variable human and mosquito populations. Mathematical and computer modeling, 32 (7), (2000), 747-763.
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[18] Purnachandra Rao Koya and Dejen Ketema Mamo, Ebola Epidemic Disease: Modelling, Stability Analysis, Spread Control Technique, Simulation Study and Data Fitting, Journal of Multidisciplinary Engineering Science and Technology (JMEST), Vol. 2, Issue 3, March 2015, pp 476 – 84. http://www.jmest.org/wp-content/uploads/JMESTN42350548.pdf.
[19] O. J. Diekmann (1990), "Mathematical Biology" Vol. 28, Pp. 365–382.
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  • APA Style

    Fekadu Tadege Kobe. (2020). Mathematical Model of Controlling the Spread of Malaria Disease Using Intervention Strategies. Pure and Applied Mathematics Journal, 9(6), 101-108. https://doi.org/10.11648/j.pamj.20200906.11

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    ACS Style

    Fekadu Tadege Kobe. Mathematical Model of Controlling the Spread of Malaria Disease Using Intervention Strategies. Pure Appl. Math. J. 2020, 9(6), 101-108. doi: 10.11648/j.pamj.20200906.11

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    AMA Style

    Fekadu Tadege Kobe. Mathematical Model of Controlling the Spread of Malaria Disease Using Intervention Strategies. Pure Appl Math J. 2020;9(6):101-108. doi: 10.11648/j.pamj.20200906.11

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  • @article{10.11648/j.pamj.20200906.11,
      author = {Fekadu Tadege Kobe},
      title = {Mathematical Model of Controlling the Spread of Malaria Disease Using Intervention Strategies},
      journal = {Pure and Applied Mathematics Journal},
      volume = {9},
      number = {6},
      pages = {101-108},
      doi = {10.11648/j.pamj.20200906.11},
      url = {https://doi.org/10.11648/j.pamj.20200906.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20200906.11},
      abstract = {This paper proposes and analyses a basic deterministic mathematical model to investigate Simulation for controlling the spread of malaria Diseases Transmission dynamics. The model has seven non-linear differential equations which describe the control of malaria with two state variables for mosquito’s populations and five state variables for human’s population. To represent the classification of human population we have included protection and treatment compartments to the basic SIR epidemic model and extended it to SPITR model and to introduce the new SPITR modified model by adding vaccination for the transmission dynamics of malaria with four time dependent control measures in Ethiopia Insecticide treated bed nets (ITNS), Treatments, Indoor Residual Spray (IRs) and Intermittent preventive treatment of malaria in pregnancy (IPTP). The models are analyzed qualitatively to determine criteria for control of a malaria transmission dynamics and are used to calculate the basic reproduction R0. The equilibria of malaria models are determined. In addition to having a disease-free equilibrium, which is globally asymptotically stable when the R0<1, the basic malaria model manifest one's possession of (a quality of) the phenomenon of backward bifurcation where a stable disease-free equilibrium co-exists (at the same time) with a stable endemic equilibrium for a certain range of associated reproduction number less than one. The results also designing the effects of some model parameters, the infection rate and biting rate. The numerical analysis and numerical simulation results of the model suggested that the most effective strategies for controlling or eradicating the spread of malaria were suggest using insecticide treated bed nets, indoor residual spraying, prompt effective diagnosis and treatment of infected individuals with vaccination is more effective for children.},
     year = {2020}
    }
    

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    AU  - Fekadu Tadege Kobe
    Y1  - 2020/11/11
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    AB  - This paper proposes and analyses a basic deterministic mathematical model to investigate Simulation for controlling the spread of malaria Diseases Transmission dynamics. The model has seven non-linear differential equations which describe the control of malaria with two state variables for mosquito’s populations and five state variables for human’s population. To represent the classification of human population we have included protection and treatment compartments to the basic SIR epidemic model and extended it to SPITR model and to introduce the new SPITR modified model by adding vaccination for the transmission dynamics of malaria with four time dependent control measures in Ethiopia Insecticide treated bed nets (ITNS), Treatments, Indoor Residual Spray (IRs) and Intermittent preventive treatment of malaria in pregnancy (IPTP). The models are analyzed qualitatively to determine criteria for control of a malaria transmission dynamics and are used to calculate the basic reproduction R0. The equilibria of malaria models are determined. In addition to having a disease-free equilibrium, which is globally asymptotically stable when the R0<1, the basic malaria model manifest one's possession of (a quality of) the phenomenon of backward bifurcation where a stable disease-free equilibrium co-exists (at the same time) with a stable endemic equilibrium for a certain range of associated reproduction number less than one. The results also designing the effects of some model parameters, the infection rate and biting rate. The numerical analysis and numerical simulation results of the model suggested that the most effective strategies for controlling or eradicating the spread of malaria were suggest using insecticide treated bed nets, indoor residual spraying, prompt effective diagnosis and treatment of infected individuals with vaccination is more effective for children.
    VL  - 9
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Author Information
  • Department of Mathematics, College of Natural and Computational Science, Wachemo University, Hossana, Ethiopia

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