Mathematical Malaria Model Focusing on the Effects of Partial Immunity, Strong Immunity, Drug Resistance and Intensive Treatment

Grace Maithya; Virginia Kitetu; Isaac Okwany

doi:doi:10.11648/j.mma.20251001.11

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Mathematical Malaria Model Focusing on the Effects of Partial Immunity, Strong Immunity, Drug Resistance and Intensive Treatment

Grace Maithya^*, Virginia Kitetu, Isaac Okwany

Published in Mathematical Modelling and Applications (Volume 10, Issue 1)

Received: 19 March 2025 Accepted: 3 April 2025 Published: 3 June 2025

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Abstract

Malaria is a public health problem that has affected many countries across the continent. To address this problem, a malaria mathematical model on assessing the impact of strong and weak immunity was investigated. In addition to that drug resistance and intensive treatment analysis was also analyzed between human and mosquito population by the use of appropriate and standard procedures. A malaria model was developed where strong immunity, and weak immunity parameters were incorporated. A variable of drug resistance was also incorporated to describe the rates of transmission of human and mosquito populations. The basic reproductive number was derived using the Next Generation Matrix Method. The stability of the basic reproductive number was checked by use of the Jacobian Matrix. The disease Free equilibrium was found to be locally asymptotically stable as the basic reproductive number is less than one and unstable if greater than one. The results were found that increased immunity, and intensive treatment helped reduce the number of infections and increased recoveries. This study will be useful to the government and non governmental organizations because they will do intensive treatment to those who have resistance malaria infections and low immunity. The government will also give immune boosters so that drug resistance can stop and increase immunity hence leading to high recoveries. The mathematical malaria modelers will use this study as reference in their research.

Published in	Mathematical Modelling and Applications (Volume 10, Issue 1)
DOI	10.11648/j.mma.20251001.11
Page(s)	1-13
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), 2025. Published by Science Publishing Group

Keywords

Numerical Simulation, Malaria, Mathematical Modeling, Immunity, Drug Resistance, and Intensive Treatment

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APA Style

Maithya, G., Kitetu, V., Okwany, I. (2025). Mathematical Malaria Model Focusing on the Effects of Partial Immunity, Strong Immunity, Drug Resistance and Intensive Treatment. Mathematical Modelling and Applications, 10(1), 1-13. https://doi.org/10.11648/j.mma.20251001.11

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ACS Style

Maithya, G.; Kitetu, V.; Okwany, I. Mathematical Malaria Model Focusing on the Effects of Partial Immunity, Strong Immunity, Drug Resistance and Intensive Treatment. Math. Model. Appl. 2025, 10(1), 1-13. doi: 10.11648/j.mma.20251001.11

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AMA Style

Maithya G, Kitetu V, Okwany I. Mathematical Malaria Model Focusing on the Effects of Partial Immunity, Strong Immunity, Drug Resistance and Intensive Treatment. Math Model Appl. 2025;10(1):1-13. doi: 10.11648/j.mma.20251001.11

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@article{10.11648/j.mma.20251001.11,
  author = {Grace Maithya and Virginia Kitetu and Isaac Okwany},
  title = {Mathematical Malaria Model Focusing on the Effects of Partial Immunity, Strong Immunity, Drug Resistance and Intensive Treatment},
  journal = {Mathematical Modelling and Applications},
  volume = {10},
  number = {1},
  pages = {1-13},
  doi = {10.11648/j.mma.20251001.11},
  url = {https://doi.org/10.11648/j.mma.20251001.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20251001.11},
  abstract = {Malaria is a public health problem that has affected many countries across the continent. To address this problem, a malaria mathematical model on assessing the impact of strong and weak immunity was investigated. In addition to that drug resistance and intensive treatment analysis was also analyzed between human and mosquito population by the use of appropriate and standard procedures. A malaria model was developed where strong immunity, and weak immunity parameters were incorporated. A variable of drug resistance was also incorporated to describe the rates of transmission of human and mosquito populations. The basic reproductive number was derived using the Next Generation Matrix Method. The stability of the basic reproductive number was checked by use of the Jacobian Matrix. The disease Free equilibrium was found to be locally asymptotically stable as the basic reproductive number is less than one and unstable if greater than one. The results were found that increased immunity, and intensive treatment helped reduce the number of infections and increased recoveries. This study will be useful to the government and non governmental organizations because they will do intensive treatment to those who have resistance malaria infections and low immunity. The government will also give immune boosters so that drug resistance can stop and increase immunity hence leading to high recoveries. The mathematical malaria modelers will use this study as reference in their research.},
 year = {2025}
}

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TY - JOUR
T1 - Mathematical Malaria Model Focusing on the Effects of Partial Immunity, Strong Immunity, Drug Resistance and Intensive Treatment
AU - Grace Maithya
AU - Virginia Kitetu
AU - Isaac Okwany
Y1 - 2025/06/03
PY - 2025
N1 - https://doi.org/10.11648/j.mma.20251001.11
DO - 10.11648/j.mma.20251001.11
T2 - Mathematical Modelling and Applications
JF - Mathematical Modelling and Applications
JO - Mathematical Modelling and Applications
SP - 1
EP - 13
PB - Science Publishing Group
SN - 2575-1794
UR - https://doi.org/10.11648/j.mma.20251001.11
AB - Malaria is a public health problem that has affected many countries across the continent. To address this problem, a malaria mathematical model on assessing the impact of strong and weak immunity was investigated. In addition to that drug resistance and intensive treatment analysis was also analyzed between human and mosquito population by the use of appropriate and standard procedures. A malaria model was developed where strong immunity, and weak immunity parameters were incorporated. A variable of drug resistance was also incorporated to describe the rates of transmission of human and mosquito populations. The basic reproductive number was derived using the Next Generation Matrix Method. The stability of the basic reproductive number was checked by use of the Jacobian Matrix. The disease Free equilibrium was found to be locally asymptotically stable as the basic reproductive number is less than one and unstable if greater than one. The results were found that increased immunity, and intensive treatment helped reduce the number of infections and increased recoveries. This study will be useful to the government and non governmental organizations because they will do intensive treatment to those who have resistance malaria infections and low immunity. The government will also give immune boosters so that drug resistance can stop and increase immunity hence leading to high recoveries. The mathematical malaria modelers will use this study as reference in their research.
VL - 10
IS - 1
ER -

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Author Information

Grace Maithya

Department of Mathematics and Actuarial Science, Faculty of Science, The Catholic University of Eastern Africa, Nairobi, Kenya

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Virginia Kitetu

Department of Mathematics and Actuarial Science, Faculty of Science, The Catholic University of Eastern Africa, Nairobi, Kenya

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Isaac Okwany

Department of Mathematics and Actuarial Science, Faculty of Science, The Catholic University of Eastern Africa, Nairobi, Kenya

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Plain Text BibTeX RIS

APA Style

Maithya, G., Kitetu, V., Okwany, I. (2025). Mathematical Malaria Model Focusing on the Effects of Partial Immunity, Strong Immunity, Drug Resistance and Intensive Treatment. Mathematical Modelling and Applications, 10(1), 1-13. https://doi.org/10.11648/j.mma.20251001.11

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ACS Style

Maithya, G.; Kitetu, V.; Okwany, I. Mathematical Malaria Model Focusing on the Effects of Partial Immunity, Strong Immunity, Drug Resistance and Intensive Treatment. Math. Model. Appl. 2025, 10(1), 1-13. doi: 10.11648/j.mma.20251001.11

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AMA Style

Maithya G, Kitetu V, Okwany I. Mathematical Malaria Model Focusing on the Effects of Partial Immunity, Strong Immunity, Drug Resistance and Intensive Treatment. Math Model Appl. 2025;10(1):1-13. doi: 10.11648/j.mma.20251001.11

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@article{10.11648/j.mma.20251001.11,
  author = {Grace Maithya and Virginia Kitetu and Isaac Okwany},
  title = {Mathematical Malaria Model Focusing on the Effects of Partial Immunity, Strong Immunity, Drug Resistance and Intensive Treatment},
  journal = {Mathematical Modelling and Applications},
  volume = {10},
  number = {1},
  pages = {1-13},
  doi = {10.11648/j.mma.20251001.11},
  url = {https://doi.org/10.11648/j.mma.20251001.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20251001.11},
  abstract = {Malaria is a public health problem that has affected many countries across the continent. To address this problem, a malaria mathematical model on assessing the impact of strong and weak immunity was investigated. In addition to that drug resistance and intensive treatment analysis was also analyzed between human and mosquito population by the use of appropriate and standard procedures. A malaria model was developed where strong immunity, and weak immunity parameters were incorporated. A variable of drug resistance was also incorporated to describe the rates of transmission of human and mosquito populations. The basic reproductive number was derived using the Next Generation Matrix Method. The stability of the basic reproductive number was checked by use of the Jacobian Matrix. The disease Free equilibrium was found to be locally asymptotically stable as the basic reproductive number is less than one and unstable if greater than one. The results were found that increased immunity, and intensive treatment helped reduce the number of infections and increased recoveries. This study will be useful to the government and non governmental organizations because they will do intensive treatment to those who have resistance malaria infections and low immunity. The government will also give immune boosters so that drug resistance can stop and increase immunity hence leading to high recoveries. The mathematical malaria modelers will use this study as reference in their research.},
 year = {2025}
}

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