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

Fekadu Tadege Kobe

doi:doi:10.11648/j.pamj.20200906.11

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

Fekadu Tadege Kobe

Published in Pure and Applied Mathematics Journal (Volume 9, Issue 6)

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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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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TY  - JOUR
T1  - Mathematical Model of Controlling the Spread of Malaria Disease Using Intervention Strategies
AU  - Fekadu Tadege Kobe
Y1  - 2020/11/11
PY  - 2020
N1  - https://doi.org/10.11648/j.pamj.20200906.11
DO  - 10.11648/j.pamj.20200906.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 101
EP  - 108
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20200906.11
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
IS  - 6
ER  -

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Author Information

Fekadu Tadege Kobe

Department of Mathematics, College of Natural and Computational Science, Wachemo University, Hossana, Ethiopia

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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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - Mathematical Model of Controlling the Spread of Malaria Disease Using Intervention Strategies
AU  - Fekadu Tadege Kobe
Y1  - 2020/11/11
PY  - 2020
N1  - https://doi.org/10.11648/j.pamj.20200906.11
DO  - 10.11648/j.pamj.20200906.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 101
EP  - 108
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20200906.11
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
IS  - 6
ER  -

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