Mathematical Model for Coinfection of HIV/AIDS and Kaposi’s Sarcoma with Treatment

Joy Teng’an Juma; Isaac Chepkwony; Abayomi Samuel Oke

doi:doi:10.11648/j.mcs.20230801.11

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Mathematical Model for Coinfection of HIV/AIDS and Kaposi’s Sarcoma with Treatment

Joy Teng’an Juma, Isaac Chepkwony, Abayomi Samuel Oke

Published in Mathematics and Computer Science (Volume 8, Issue 1)

Received: 7 December 2022 Accepted: 26 December 2022 Published: 17 January 2023

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Abstract

HIV destroys T-cells in order to target the body's defence mechanism. Without treatment HIV infection advances in stages causing destruction and reduction in T-cells thus, rendering the body incapable of fighting other infections such as respiratory infections, sexually transmitted diseases and some cancers. Kaposi’s sarcoma is the cancer that allows a tumour to grow in an HIV patient and its presence in a patient is an indication that HIV has fully developed into AIDS in the patient. Research has indicated that AIDS-associated Kaposi Sarcoma was on the rise in sub-Saharan Africa until the introduction of Antiretroviral Therapy (ART). The Kenyan community has struggled in the past decade to combat the spread of HIV/AIDS and successes have been recorded in many areas. However, Kaposi Sarcoma, an opportunistic infection, has continued to rise steadily through the years. In this study, a simple model for the coinfection of HIV/AIDS and KS is developed and studied. The model solution is explored for positivity and boundedness while the DFE point is determined for stability where it was verified that the infection-free equilibrium E₀ is locally asymptotically stable when . The NGM is used to derive the basic reproduction number of the model. By providing treatment to the HIV and the co-infected population immune system is strengthened and thus progression rate to AIDS is reduced.

Published in	Mathematics and Computer Science (Volume 8, Issue 1)
DOI	10.11648/j.mcs.20230801.11
Page(s)	1-10
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), 2024. Published by Science Publishing Group

Keywords

HIV/AIDS, Coinfection, Kaposi’s Sarcoma, Treatment, Reproduction Number

References

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APA Style

Joy Teng’an Juma, Isaac Chepkwony, Abayomi Samuel Oke. (2023). Mathematical Model for Coinfection of HIV/AIDS and Kaposi’s Sarcoma with Treatment. Mathematics and Computer Science, 8(1), 1-10. https://doi.org/10.11648/j.mcs.20230801.11

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ACS Style

Joy Teng’an Juma; Isaac Chepkwony; Abayomi Samuel Oke. Mathematical Model for Coinfection of HIV/AIDS and Kaposi’s Sarcoma with Treatment. Math. Comput. Sci. 2023, 8(1), 1-10. doi: 10.11648/j.mcs.20230801.11

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AMA Style

Joy Teng’an Juma, Isaac Chepkwony, Abayomi Samuel Oke. Mathematical Model for Coinfection of HIV/AIDS and Kaposi’s Sarcoma with Treatment. Math Comput Sci. 2023;8(1):1-10. doi: 10.11648/j.mcs.20230801.11

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@article{10.11648/j.mcs.20230801.11,
  author = {Joy Teng’an Juma and Isaac Chepkwony and Abayomi Samuel Oke},
  title = {Mathematical Model for Coinfection of HIV/AIDS and Kaposi’s Sarcoma with Treatment},
  journal = {Mathematics and Computer Science},
  volume = {8},
  number = {1},
  pages = {1-10},
  doi = {10.11648/j.mcs.20230801.11},
  url = {https://doi.org/10.11648/j.mcs.20230801.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20230801.11},
  abstract = {HIV destroys T-cells in order to target the body's defence mechanism. Without treatment HIV infection advances in stages causing destruction and reduction in T-cells thus, rendering the body incapable of fighting other infections such as respiratory infections, sexually transmitted diseases and some cancers. Kaposi’s sarcoma is the cancer that allows a tumour to grow in an HIV patient and its presence in a patient is an indication that HIV has fully developed into AIDS in the patient. Research has indicated that AIDS-associated Kaposi Sarcoma was on the rise in sub-Saharan Africa until the introduction of Antiretroviral Therapy (ART). The Kenyan community has struggled in the past decade to combat the spread of HIV/AIDS and successes have been recorded in many areas. However, Kaposi Sarcoma, an opportunistic infection, has continued to rise steadily through the years. In this study, a simple model for the coinfection of HIV/AIDS and KS is developed and studied. The model solution is explored for positivity and boundedness while the DFE point is determined for stability where it was verified that the infection-free equilibrium E0 is locally asymptotically stable when . The NGM is used to derive the basic reproduction number of the model. By providing treatment to the HIV and the co-infected population immune system is strengthened and thus progression rate to AIDS is reduced.},
 year = {2023}
}

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TY - JOUR
T1 - Mathematical Model for Coinfection of HIV/AIDS and Kaposi’s Sarcoma with Treatment
AU - Joy Teng’an Juma
AU - Isaac Chepkwony
AU - Abayomi Samuel Oke
Y1 - 2023/01/17
PY - 2023
N1 - https://doi.org/10.11648/j.mcs.20230801.11
DO - 10.11648/j.mcs.20230801.11
T2 - Mathematics and Computer Science
JF - Mathematics and Computer Science
JO - Mathematics and Computer Science
SP - 1
EP - 10
PB - Science Publishing Group
SN - 2575-6028
UR - https://doi.org/10.11648/j.mcs.20230801.11
AB - HIV destroys T-cells in order to target the body's defence mechanism. Without treatment HIV infection advances in stages causing destruction and reduction in T-cells thus, rendering the body incapable of fighting other infections such as respiratory infections, sexually transmitted diseases and some cancers. Kaposi’s sarcoma is the cancer that allows a tumour to grow in an HIV patient and its presence in a patient is an indication that HIV has fully developed into AIDS in the patient. Research has indicated that AIDS-associated Kaposi Sarcoma was on the rise in sub-Saharan Africa until the introduction of Antiretroviral Therapy (ART). The Kenyan community has struggled in the past decade to combat the spread of HIV/AIDS and successes have been recorded in many areas. However, Kaposi Sarcoma, an opportunistic infection, has continued to rise steadily through the years. In this study, a simple model for the coinfection of HIV/AIDS and KS is developed and studied. The model solution is explored for positivity and boundedness while the DFE point is determined for stability where it was verified that the infection-free equilibrium E0 is locally asymptotically stable when . The NGM is used to derive the basic reproduction number of the model. By providing treatment to the HIV and the co-infected population immune system is strengthened and thus progression rate to AIDS is reduced.
VL - 8
IS - 1
ER -

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Author Information

Joy Teng’an Juma

Department of Mathematics and Actuarial Science, Kenyatta University, Nairobi, Kenya
Isaac Chepkwony

Department of Mathematics and Actuarial Science, Kenyatta University, Nairobi, Kenya
Abayomi Samuel Oke

Department of Mathematics and Actuarial Science, Kenyatta University, Nairobi, Kenya

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Plain Text BibTeX RIS

APA Style

Joy Teng’an Juma, Isaac Chepkwony, Abayomi Samuel Oke. (2023). Mathematical Model for Coinfection of HIV/AIDS and Kaposi’s Sarcoma with Treatment. Mathematics and Computer Science, 8(1), 1-10. https://doi.org/10.11648/j.mcs.20230801.11

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ACS Style

Joy Teng’an Juma; Isaac Chepkwony; Abayomi Samuel Oke. Mathematical Model for Coinfection of HIV/AIDS and Kaposi’s Sarcoma with Treatment. Math. Comput. Sci. 2023, 8(1), 1-10. doi: 10.11648/j.mcs.20230801.11

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AMA Style

Joy Teng’an Juma, Isaac Chepkwony, Abayomi Samuel Oke. Mathematical Model for Coinfection of HIV/AIDS and Kaposi’s Sarcoma with Treatment. Math Comput Sci. 2023;8(1):1-10. doi: 10.11648/j.mcs.20230801.11

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@article{10.11648/j.mcs.20230801.11,
  author = {Joy Teng’an Juma and Isaac Chepkwony and Abayomi Samuel Oke},
  title = {Mathematical Model for Coinfection of HIV/AIDS and Kaposi’s Sarcoma with Treatment},
  journal = {Mathematics and Computer Science},
  volume = {8},
  number = {1},
  pages = {1-10},
  doi = {10.11648/j.mcs.20230801.11},
  url = {https://doi.org/10.11648/j.mcs.20230801.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20230801.11},
  abstract = {HIV destroys T-cells in order to target the body's defence mechanism. Without treatment HIV infection advances in stages causing destruction and reduction in T-cells thus, rendering the body incapable of fighting other infections such as respiratory infections, sexually transmitted diseases and some cancers. Kaposi’s sarcoma is the cancer that allows a tumour to grow in an HIV patient and its presence in a patient is an indication that HIV has fully developed into AIDS in the patient. Research has indicated that AIDS-associated Kaposi Sarcoma was on the rise in sub-Saharan Africa until the introduction of Antiretroviral Therapy (ART). The Kenyan community has struggled in the past decade to combat the spread of HIV/AIDS and successes have been recorded in many areas. However, Kaposi Sarcoma, an opportunistic infection, has continued to rise steadily through the years. In this study, a simple model for the coinfection of HIV/AIDS and KS is developed and studied. The model solution is explored for positivity and boundedness while the DFE point is determined for stability where it was verified that the infection-free equilibrium E0 is locally asymptotically stable when . The NGM is used to derive the basic reproduction number of the model. By providing treatment to the HIV and the co-infected population immune system is strengthened and thus progression rate to AIDS is reduced.},
 year = {2023}
}

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