The control of opportunistic infections among HIV infected individuals should be one of the major public health concerns in reducing mortality rate of individuals living with HIV/AIDS. In this study a deterministic co-infection mathematical model is developed to provide a quantification of treatment at each contagious stage against Pneumocystis Pneumonia (PCP) among HIV infected individuals on ART. The goal is to minimize the co-infection burden by putting the curable PCP under control. The disease-free equilibria for the HIV/AIDS sub-model, PCP sub-model and the co-infection model are shown to be locally asymptotically stable when their associated disease threshold parameter is less than a unity. By use of suitable Lyapunov functions, the endemic equilibria corresponding to HIV/AIDS and PCP sub-models are globally asymptotically stable whenever the HIV/AIDS related basic reproduction number R0H and the PCP related reproduction number R0P are respectively greater than a unity. The sensitivity analysis results implicate that the effective contact rates are the main mechanisms fueling the proliferation of the two diseases and on the other hand treatment efforts play an important role in reducing the incidence. The model numerical results reveal that PCP carriers have a considerable contribution in the transmission dynamics of PCP. Furthermore, treatment of PCP at all contagious phases significantly reduces the burden with HIV/AIDS and PCP co-infection.
| Published in | Science Journal of Applied Mathematics and Statistics (Volume 12, Issue 4) |
| DOI | 10.11648/j.sjams.20241204.11 |
| Page(s) | 48-63 |
| 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 |
HIV/AIDS, PCP Carriers, Basic Reproduction Number(s), Co-infection, Stability, Sensitivity Analysis
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APA Style
Byamukama, M., Kajunguri, D., Karuhanga, M. (2024). A Mathematical Model for the Co-infection Dynamics of Pneumocystis Pneumonia and HIV/AIDS with Treatment. Science Journal of Applied Mathematics and Statistics, 12(4), 48-63. https://doi.org/10.11648/j.sjams.20241204.11
ACS Style
Byamukama, M.; Kajunguri, D.; Karuhanga, M. A Mathematical Model for the Co-infection Dynamics of Pneumocystis Pneumonia and HIV/AIDS with Treatment. Sci. J. Appl. Math. Stat. 2024, 12(4), 48-63. doi: 10.11648/j.sjams.20241204.11
AMA Style
Byamukama M, Kajunguri D, Karuhanga M. A Mathematical Model for the Co-infection Dynamics of Pneumocystis Pneumonia and HIV/AIDS with Treatment. Sci J Appl Math Stat. 2024;12(4):48-63. doi: 10.11648/j.sjams.20241204.11
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Download@article{10.11648/j.sjams.20241204.11,
author = {Michael Byamukama and Damian Kajunguri and Martin Karuhanga},
title = {A Mathematical Model for the Co-infection Dynamics of Pneumocystis Pneumonia and HIV/AIDS with Treatment},
journal = {Science Journal of Applied Mathematics and Statistics},
volume = {12},
number = {4},
pages = {48-63},
doi = {10.11648/j.sjams.20241204.11},
url = {https://doi.org/10.11648/j.sjams.20241204.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20241204.11},
abstract = {The control of opportunistic infections among HIV infected individuals should be one of the major public health concerns in reducing mortality rate of individuals living with HIV/AIDS. In this study a deterministic co-infection mathematical model is developed to provide a quantification of treatment at each contagious stage against Pneumocystis Pneumonia (PCP) among HIV infected individuals on ART. The goal is to minimize the co-infection burden by putting the curable PCP under control. The disease-free equilibria for the HIV/AIDS sub-model, PCP sub-model and the co-infection model are shown to be locally asymptotically stable when their associated disease threshold parameter is less than a unity. By use of suitable Lyapunov functions, the endemic equilibria corresponding to HIV/AIDS and PCP sub-models are globally asymptotically stable whenever the HIV/AIDS related basic reproduction number R0H and the PCP related reproduction number R0P are respectively greater than a unity. The sensitivity analysis results implicate that the effective contact rates are the main mechanisms fueling the proliferation of the two diseases and on the other hand treatment efforts play an important role in reducing the incidence. The model numerical results reveal that PCP carriers have a considerable contribution in the transmission dynamics of PCP. Furthermore, treatment of PCP at all contagious phases significantly reduces the burden with HIV/AIDS and PCP co-infection.},
year = {2024}
}
TY - JOUR T1 - A Mathematical Model for the Co-infection Dynamics of Pneumocystis Pneumonia and HIV/AIDS with Treatment AU - Michael Byamukama AU - Damian Kajunguri AU - Martin Karuhanga Y1 - 2024/07/27 PY - 2024 N1 - https://doi.org/10.11648/j.sjams.20241204.11 DO - 10.11648/j.sjams.20241204.11 T2 - Science Journal of Applied Mathematics and Statistics JF - Science Journal of Applied Mathematics and Statistics JO - Science Journal of Applied Mathematics and Statistics SP - 48 EP - 63 PB - Science Publishing Group SN - 2376-9513 UR - https://doi.org/10.11648/j.sjams.20241204.11 AB - The control of opportunistic infections among HIV infected individuals should be one of the major public health concerns in reducing mortality rate of individuals living with HIV/AIDS. In this study a deterministic co-infection mathematical model is developed to provide a quantification of treatment at each contagious stage against Pneumocystis Pneumonia (PCP) among HIV infected individuals on ART. The goal is to minimize the co-infection burden by putting the curable PCP under control. The disease-free equilibria for the HIV/AIDS sub-model, PCP sub-model and the co-infection model are shown to be locally asymptotically stable when their associated disease threshold parameter is less than a unity. By use of suitable Lyapunov functions, the endemic equilibria corresponding to HIV/AIDS and PCP sub-models are globally asymptotically stable whenever the HIV/AIDS related basic reproduction number R0H and the PCP related reproduction number R0P are respectively greater than a unity. The sensitivity analysis results implicate that the effective contact rates are the main mechanisms fueling the proliferation of the two diseases and on the other hand treatment efforts play an important role in reducing the incidence. The model numerical results reveal that PCP carriers have a considerable contribution in the transmission dynamics of PCP. Furthermore, treatment of PCP at all contagious phases significantly reduces the burden with HIV/AIDS and PCP co-infection. VL - 12 IS - 4 ER -
Department of Mathematics, Mbarara University of Science and Technology, Mbarara, Uganda
Department of Mathematics, Kabale University, Kabale, Uganda
Department of Mathematics, Mbarara University of Science and Technology, Mbarara, Uganda
