Modeling the Dynamics of Endemic Malaria Transmission with the Effects of Control Measure

Dereje Gutema Edossa; Alemu Geleta Wedajo; Purnachandra Rao Koya

doi:doi:10.11648/j.ajam.20200803.17

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Modeling the Dynamics of Endemic Malaria Transmission with the Effects of Control Measure

Dereje Gutema Edossa, Alemu Geleta Wedajo, Purnachandra Rao Koya

Published in American Journal of Applied Mathematics (Volume 8, Issue 3)

Received: 27 December 2019 Accepted: 3 June 2020 Published: 17 June 2020

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Abstract

Malaria is an infectious disease caused by Plasmodium parasite and is transmitted among humans through bites of female Anopheles mosquitoes. It is estimated 216 million people suffered from malaria in 2016, with over 400,000 deaths mainly in sub-Saharan Africa. A number of control measures have been put in place: most importantly the insecticide treated net (ITN) and indoor residual sprayings (IRS) of insecticide. Currently, the emergence and spread of resistance in mosquito populations against insecticides is the most common and widely spread .It is also poses a key obstacle to malaria control as well as jeopardizing the effects of the most efficient malaria control interventions. A mathematical model that incorporates the evolution of insecticide resistance and its impact on endemic malaria transmission i.e., effects of indoor residual sprayings (IRS) on the insecticide resistant and sensitive malaria vector strains as a control strategy is incorporated and analyzed. The object of the study is to understand qualitatively the factor that have more influence for the emergence and spread of resistance of malaria vectors against IRS and their impacts on the efficacy of IRS. Based on a Ross-Macdonald derivation of malaria model the effective reproduction number〖 R〗_e isused to assess the effects of IRS in the qualitative analysis of the model. The existence and stability of the disease-free and endemic equilibria of the model are studied. It is established that the malaria can be brought under control as long as R_(e )is kept below the threshold value. Numerical simulations studies are conducted so as to determine the role played by key parameters of the model. The public health implications of the results include: (i) every effort should be taken to minimize the evolution of insecticide resistance due to malaria control interventions failure and (ii) at least a combination of two types of different control measures and followed by rotation of intervention strategies could be more realistic to minimize the number of resistant malaria vector strains and essential in reducing the malaria burden in the community.

Published in	American Journal of Applied Mathematics (Volume 8, Issue 3)
DOI	10.11648/j.ajam.20200803.17
Page(s)	158-170
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

Endemic Malaria, Infectious, Insecticide, Emergence, Resistance, Modeling, Mosquito

References

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APA Style

Dereje Gutema Edossa, Alemu Geleta Wedajo, Purnachandra Rao Koya. (2020). Modeling the Dynamics of Endemic Malaria Transmission with the Effects of Control Measure. American Journal of Applied Mathematics, 8(3), 158-170. https://doi.org/10.11648/j.ajam.20200803.17

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ACS Style

Dereje Gutema Edossa; Alemu Geleta Wedajo; Purnachandra Rao Koya. Modeling the Dynamics of Endemic Malaria Transmission with the Effects of Control Measure. Am. J. Appl. Math. 2020, 8(3), 158-170. doi: 10.11648/j.ajam.20200803.17

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AMA Style

Dereje Gutema Edossa, Alemu Geleta Wedajo, Purnachandra Rao Koya. Modeling the Dynamics of Endemic Malaria Transmission with the Effects of Control Measure. Am J Appl Math. 2020;8(3):158-170. doi: 10.11648/j.ajam.20200803.17

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@article{10.11648/j.ajam.20200803.17,
  author = {Dereje Gutema Edossa and Alemu Geleta Wedajo and Purnachandra Rao Koya},
  title = {Modeling the Dynamics of Endemic Malaria Transmission with the Effects of Control Measure},
  journal = {American Journal of Applied Mathematics},
  volume = {8},
  number = {3},
  pages = {158-170},
  doi = {10.11648/j.ajam.20200803.17},
  url = {https://doi.org/10.11648/j.ajam.20200803.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20200803.17},
  abstract = {Malaria is an infectious disease caused by Plasmodium parasite and is transmitted among humans through bites of female Anopheles mosquitoes. It is estimated 216 million people suffered from malaria in 2016, with over 400,000 deaths mainly in sub-Saharan Africa. A number of control measures have been put in place: most importantly the insecticide treated net (ITN) and indoor residual sprayings (IRS) of insecticide. Currently, the emergence and spread of resistance in mosquito populations against insecticides is the most common and widely spread .It is also poses a key obstacle to malaria control as well as jeopardizing the effects of the most efficient malaria control interventions. A mathematical model that incorporates the evolution of insecticide resistance and its impact on endemic malaria transmission i.e., effects of indoor residual sprayings (IRS) on the insecticide resistant and sensitive malaria vector strains as a control strategy is incorporated and analyzed. The object of the study is to understand qualitatively the factor that have more influence for the emergence and spread of resistance of malaria vectors against IRS and their impacts on the efficacy of IRS. Based on a Ross-Macdonald derivation of malaria model the effective reproduction number〖 R〗_e isused to assess the effects of IRS in the qualitative analysis of the model. The existence and stability of the disease-free and endemic equilibria of the model are studied. It is established that the malaria can be brought under control as long as R_(e )is kept below the threshold value. Numerical simulations studies are conducted so as to determine the role played by key parameters of the model. The public health implications of the results include: (i) every effort should be taken to minimize the evolution of insecticide resistance due to malaria control interventions failure and (ii) at least a combination of two types of different control measures and followed by rotation of intervention strategies could be more realistic to minimize the number of resistant malaria vector strains and essential in reducing the malaria burden in the community.},
 year = {2020}
}

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TY  - JOUR
T1  - Modeling the Dynamics of Endemic Malaria Transmission with the Effects of Control Measure
AU  - Dereje Gutema Edossa
AU  - Alemu Geleta Wedajo
AU  - Purnachandra Rao Koya
Y1  - 2020/06/17
PY  - 2020
N1  - https://doi.org/10.11648/j.ajam.20200803.17
DO  - 10.11648/j.ajam.20200803.17
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 158
EP  - 170
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20200803.17
AB  - Malaria is an infectious disease caused by Plasmodium parasite and is transmitted among humans through bites of female Anopheles mosquitoes. It is estimated 216 million people suffered from malaria in 2016, with over 400,000 deaths mainly in sub-Saharan Africa. A number of control measures have been put in place: most importantly the insecticide treated net (ITN) and indoor residual sprayings (IRS) of insecticide. Currently, the emergence and spread of resistance in mosquito populations against insecticides is the most common and widely spread .It is also poses a key obstacle to malaria control as well as jeopardizing the effects of the most efficient malaria control interventions. A mathematical model that incorporates the evolution of insecticide resistance and its impact on endemic malaria transmission i.e., effects of indoor residual sprayings (IRS) on the insecticide resistant and sensitive malaria vector strains as a control strategy is incorporated and analyzed. The object of the study is to understand qualitatively the factor that have more influence for the emergence and spread of resistance of malaria vectors against IRS and their impacts on the efficacy of IRS. Based on a Ross-Macdonald derivation of malaria model the effective reproduction number〖 R〗_e isused to assess the effects of IRS in the qualitative analysis of the model. The existence and stability of the disease-free and endemic equilibria of the model are studied. It is established that the malaria can be brought under control as long as R_(e )is kept below the threshold value. Numerical simulations studies are conducted so as to determine the role played by key parameters of the model. The public health implications of the results include: (i) every effort should be taken to minimize the evolution of insecticide resistance due to malaria control interventions failure and (ii) at least a combination of two types of different control measures and followed by rotation of intervention strategies could be more realistic to minimize the number of resistant malaria vector strains and essential in reducing the malaria burden in the community.
VL  - 8
IS  - 3
ER  -

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Author Information

Dereje Gutema Edossa

Department of Mathematics, Wollega University, Nekemte, Ethiopia
Alemu Geleta Wedajo

Department of Mathematics, Wollega University, Nekemte, Ethiopia
Purnachandra Rao Koya

Department of Mathematics, Wollega University, Nekemte, Ethiopia

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APA Style

Dereje Gutema Edossa, Alemu Geleta Wedajo, Purnachandra Rao Koya. (2020). Modeling the Dynamics of Endemic Malaria Transmission with the Effects of Control Measure. American Journal of Applied Mathematics, 8(3), 158-170. https://doi.org/10.11648/j.ajam.20200803.17

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ACS Style

Dereje Gutema Edossa; Alemu Geleta Wedajo; Purnachandra Rao Koya. Modeling the Dynamics of Endemic Malaria Transmission with the Effects of Control Measure. Am. J. Appl. Math. 2020, 8(3), 158-170. doi: 10.11648/j.ajam.20200803.17

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AMA Style

Dereje Gutema Edossa, Alemu Geleta Wedajo, Purnachandra Rao Koya. Modeling the Dynamics of Endemic Malaria Transmission with the Effects of Control Measure. Am J Appl Math. 2020;8(3):158-170. doi: 10.11648/j.ajam.20200803.17

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@article{10.11648/j.ajam.20200803.17,
  author = {Dereje Gutema Edossa and Alemu Geleta Wedajo and Purnachandra Rao Koya},
  title = {Modeling the Dynamics of Endemic Malaria Transmission with the Effects of Control Measure},
  journal = {American Journal of Applied Mathematics},
  volume = {8},
  number = {3},
  pages = {158-170},
  doi = {10.11648/j.ajam.20200803.17},
  url = {https://doi.org/10.11648/j.ajam.20200803.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20200803.17},
  abstract = {Malaria is an infectious disease caused by Plasmodium parasite and is transmitted among humans through bites of female Anopheles mosquitoes. It is estimated 216 million people suffered from malaria in 2016, with over 400,000 deaths mainly in sub-Saharan Africa. A number of control measures have been put in place: most importantly the insecticide treated net (ITN) and indoor residual sprayings (IRS) of insecticide. Currently, the emergence and spread of resistance in mosquito populations against insecticides is the most common and widely spread .It is also poses a key obstacle to malaria control as well as jeopardizing the effects of the most efficient malaria control interventions. A mathematical model that incorporates the evolution of insecticide resistance and its impact on endemic malaria transmission i.e., effects of indoor residual sprayings (IRS) on the insecticide resistant and sensitive malaria vector strains as a control strategy is incorporated and analyzed. The object of the study is to understand qualitatively the factor that have more influence for the emergence and spread of resistance of malaria vectors against IRS and their impacts on the efficacy of IRS. Based on a Ross-Macdonald derivation of malaria model the effective reproduction number〖 R〗_e isused to assess the effects of IRS in the qualitative analysis of the model. The existence and stability of the disease-free and endemic equilibria of the model are studied. It is established that the malaria can be brought under control as long as R_(e )is kept below the threshold value. Numerical simulations studies are conducted so as to determine the role played by key parameters of the model. The public health implications of the results include: (i) every effort should be taken to minimize the evolution of insecticide resistance due to malaria control interventions failure and (ii) at least a combination of two types of different control measures and followed by rotation of intervention strategies could be more realistic to minimize the number of resistant malaria vector strains and essential in reducing the malaria burden in the community.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Modeling the Dynamics of Endemic Malaria Transmission with the Effects of Control Measure
AU  - Dereje Gutema Edossa
AU  - Alemu Geleta Wedajo
AU  - Purnachandra Rao Koya
Y1  - 2020/06/17
PY  - 2020
N1  - https://doi.org/10.11648/j.ajam.20200803.17
DO  - 10.11648/j.ajam.20200803.17
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 158
EP  - 170
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20200803.17
AB  - Malaria is an infectious disease caused by Plasmodium parasite and is transmitted among humans through bites of female Anopheles mosquitoes. It is estimated 216 million people suffered from malaria in 2016, with over 400,000 deaths mainly in sub-Saharan Africa. A number of control measures have been put in place: most importantly the insecticide treated net (ITN) and indoor residual sprayings (IRS) of insecticide. Currently, the emergence and spread of resistance in mosquito populations against insecticides is the most common and widely spread .It is also poses a key obstacle to malaria control as well as jeopardizing the effects of the most efficient malaria control interventions. A mathematical model that incorporates the evolution of insecticide resistance and its impact on endemic malaria transmission i.e., effects of indoor residual sprayings (IRS) on the insecticide resistant and sensitive malaria vector strains as a control strategy is incorporated and analyzed. The object of the study is to understand qualitatively the factor that have more influence for the emergence and spread of resistance of malaria vectors against IRS and their impacts on the efficacy of IRS. Based on a Ross-Macdonald derivation of malaria model the effective reproduction number〖 R〗_e isused to assess the effects of IRS in the qualitative analysis of the model. The existence and stability of the disease-free and endemic equilibria of the model are studied. It is established that the malaria can be brought under control as long as R_(e )is kept below the threshold value. Numerical simulations studies are conducted so as to determine the role played by key parameters of the model. The public health implications of the results include: (i) every effort should be taken to minimize the evolution of insecticide resistance due to malaria control interventions failure and (ii) at least a combination of two types of different control measures and followed by rotation of intervention strategies could be more realistic to minimize the number of resistant malaria vector strains and essential in reducing the malaria burden in the community.
VL  - 8
IS  - 3
ER  -

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