Impact of Defaulter Tracing Strategies on HIV/AIDS Dynamics: A Numerical Simulation Study

Sammy Maingi; Benjamin Kikwai; Mark Kimathi

doi:doi:10.11648/j.ijhpebs.20251101.17

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Impact of Defaulter Tracing Strategies on HIV/AIDS Dynamics: A Numerical Simulation Study

Sammy Maingi^*

, Benjamin Kikwai

, Mark Kimathi

Published in International Journal of HIV/AIDS Prevention, Education and Behavioural Science (Volume 11, Issue 1)

Received: 21 May 2025 Accepted: 13 June 2025 Published: 30 June 2025

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Abstract

Antiretroviral therapy (ART) adherence is crucial for HIV/AIDS control, yet patient default remains a significant challenge. Defaulter tracing aims to re-engage patients lost to follow-up, but its quantitative impact under varying conditions needs assessment. This study employs numerical simulations of a deterministic compartmental HIV/AIDS model to evaluate the impact of varying defaulter tracing effectiveness (DT_eff) and ART retention rates (θ) on epidemic dynamics within Kenya. The model, incorporating susceptible, infected, on-ART, not-on-ART, and under-tracing compartments, was solved using the Runge-Kutta-Fehlberg (RKF45) method with parameters informed by data. Scenarios explored DT_eff levels from 45% to 75% and retention rates (θ) from 65% to 85%. Simulation results demonstrate that increasing DT_eff significantly reduces the untreated infected population (I_NARV) and the size of the defaulter population (D_TR), while increasing the population maintained on ART (I_ARV). However, improving the retention rate (θ) showed a significant impact of reducing the need for tracing and the size of the untreated population, while substantially increasing ART coverage. The findings highlight that while effective defaulter tracing is a vital component, particularly when retention is suboptimal, improving ART retention is fundamental for long-term HIV control. This study shows the need for integrated public health strategies that combine robust, proactive retention efforts with efficient defaulter tracing mechanisms to effectively manage the HIV/AIDS epidemic.

Published in	International Journal of HIV/AIDS Prevention, Education and Behavioural Science (Volume 11, Issue 1)
DOI	10.11648/j.ijhpebs.20251101.17
Page(s)	59-67
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

HIV/AIDS, Mathematical Model, Defaulter Tracing, Basic Reproduction Number, Stability Analysis

References

[1]	Estill, J., Tweya, H., Egger, M., Wandeler, G., Feldacker, C., Johnson, L. F., Blaser, N., Vizcaya, L. S., Phiri, S. and Keiser, O., “Tracing of patients lost to follow-up and HIV transmission: mathematical modeling study based on 2 large ART programs in Malawi,” JAIDS Journal of Acquired Immune Deficiency Syndromes, vol. 65, no. 5, pp. e179–e186, 2014.
[2]	Omondi, E. O., Mbogo, R. W. and Luboobi, L. S., “Mathematical modelling of the impact of testing, treatment and control of HIV transmission in Kenya,” Cogent Mathematics & Statistics, vol. 5, no. 1, p. 1475590, 2018.
[3]	Nosyk, B., Armstrong, W. S. and Del Rio, C., “Contact tracing for COVID-19: an opportunity to reduce health disparities and end the human immunodeficiency virus/AIDS epidemic in the United States,” Clinical Infectious Diseases, vol. 71, no. 16, pp. 2259–2261, 2020.
[4]	Etoori, D., Wringe, A., Renju, J., Kabudula, C. W., Gomez-Olive, F. X. and Reniers, G., “Challenges with tracing patients on antiretroviral therapy who are late for clinic appointments in rural South Africa and recommendations for future practice,” Global Health Action, vol. 13, no. 1, p. 1755115, 2020.
[5]	Wekesa, P., Oyore, J. P., Maritim, M., et al., “Survival probability and factors associated with time to loss to follow-up and mortality among patients on antiretroviral treatment in central Kenya,” BMC Infectious Diseases, vol. 22, no. 522, 2022. https://doi.org/10.1186/s12879-022-07508-z
[6]	De Angeles, K., “PMTCT care engagement as a social practice and system: insights from an mHealth intervention and routine tracing in western Kenya,” PhD thesis, Karolinska Institutet, 2024.
[7]	UNAIDS, “Progress Towards the 95-95-95 Targets,” Global AIDS Update 2023, Joint United Nations Programme on HIV/AIDS, 2023. [Online]. Available: https://www.unaids.org/sites/default/files/media_asset/progress-towards-95-95-95_en.pdf . [Accessed: 2024-03- 15].
[8]	Young, P. W., Musingila, P., Kingwara, L., Voetsch, A. C., Zielinski-Gutierrez, E., Bulterys, M., Kim, A. A., Bronson, M. A., Parekh, B. S., Dobbs, T., et al., “HIV incidence, recent HIV infection, and associated factors, Kenya, 2007–2018,” AIDS Research and Human Retroviruses, vol. 39, no. 2, pp. 57–67, 2023.
[9]	Kemnic, T. R. and Gulick, P. G., “HIV Antiretroviral Therapy,” StatPearls [Internet], 2024.
[10]	Endebu, T., Taye, G. and Deressa, W., “Rate and predictors of loss to follow-up in HIV care in a low-resource setting: analyzing critical risk periods,” BMC Infectious Diseases, vol. 24, no. 1, pp. 1–10, 2024.
[11]	World Bank, “Kenya Population Data,” World Bank Group, 2023. [Online]. Available: https://data.worldbank.org/indicator/SP.POP.TOTL? locations=KE . [Accessed: 2024-03-15].
[12]	NSDCC, “KMoT Report - November 2024,” National Sustainable Development Coordination Committee (NSDCC), 2024. [Online]. Available: https://analytics.nsdcc.go.ke/estimates/KMoT%20Report%20-%20November-2024.pdf . [Accessed: 2024-03-15].

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APA Style

Maingi, S., Kikwai, B., Kimathi, M. (2025). Impact of Defaulter Tracing Strategies on HIV/AIDS Dynamics: A Numerical Simulation Study. International Journal of HIV/AIDS Prevention, Education and Behavioural Science, 11(1), 59-67. https://doi.org/10.11648/j.ijhpebs.20251101.17

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ACS Style

Maingi, S.; Kikwai, B.; Kimathi, M. Impact of Defaulter Tracing Strategies on HIV/AIDS Dynamics: A Numerical Simulation Study. Int. J. HIV/AIDS Prev. Educ. Behav. Sci. 2025, 11(1), 59-67. doi: 10.11648/j.ijhpebs.20251101.17

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AMA Style

Maingi S, Kikwai B, Kimathi M. Impact of Defaulter Tracing Strategies on HIV/AIDS Dynamics: A Numerical Simulation Study. Int J HIV/AIDS Prev Educ Behav Sci. 2025;11(1):59-67. doi: 10.11648/j.ijhpebs.20251101.17

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@article{10.11648/j.ijhpebs.20251101.17,
  author = {Sammy Maingi and Benjamin Kikwai and Mark Kimathi},
  title = {Impact of Defaulter Tracing Strategies on HIV/AIDS Dynamics: A Numerical Simulation Study
},
  journal = {International Journal of HIV/AIDS Prevention, Education and Behavioural Science},
  volume = {11},
  number = {1},
  pages = {59-67},
  doi = {10.11648/j.ijhpebs.20251101.17},
  url = {https://doi.org/10.11648/j.ijhpebs.20251101.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijhpebs.20251101.17},
  abstract = {Antiretroviral therapy (ART) adherence is crucial for HIV/AIDS control, yet patient default remains a significant challenge. Defaulter tracing aims to re-engage patients lost to follow-up, but its quantitative impact under varying conditions needs assessment. This study employs numerical simulations of a deterministic compartmental HIV/AIDS model to evaluate the impact of varying defaulter tracing effectiveness (DTeff) and ART retention rates (θ) on epidemic dynamics within Kenya. The model, incorporating susceptible, infected, on-ART, not-on-ART, and under-tracing compartments, was solved using the Runge-Kutta-Fehlberg (RKF45) method with parameters informed by data. Scenarios explored DTeff levels from 45% to 75% and retention rates (θ) from 65% to 85%. Simulation results demonstrate that increasing DTeff significantly reduces the untreated infected population (INARV) and the size of the defaulter population (DTR), while increasing the population maintained on ART (IARV). However, improving the retention rate (θ) showed a significant impact of reducing the need for tracing and the size of the untreated population, while substantially increasing ART coverage. The findings highlight that while effective defaulter tracing is a vital component, particularly when retention is suboptimal, improving ART retention is fundamental for long-term HIV control. This study shows the need for integrated public health strategies that combine robust, proactive retention efforts with efficient defaulter tracing mechanisms to effectively manage the HIV/AIDS epidemic.
},
 year = {2025}
}

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TY  - JOUR
T1  - Impact of Defaulter Tracing Strategies on HIV/AIDS Dynamics: A Numerical Simulation Study

AU  - Sammy Maingi
AU  - Benjamin Kikwai
AU  - Mark Kimathi
Y1  - 2025/06/30
PY  - 2025
N1  - https://doi.org/10.11648/j.ijhpebs.20251101.17
DO  - 10.11648/j.ijhpebs.20251101.17
T2  - International Journal of HIV/AIDS Prevention, Education and Behavioural Science
JF  - International Journal of HIV/AIDS Prevention, Education and Behavioural Science
JO  - International Journal of HIV/AIDS Prevention, Education and Behavioural Science
SP  - 59
EP  - 67
PB  - Science Publishing Group
SN  - 2575-5765
UR  - https://doi.org/10.11648/j.ijhpebs.20251101.17
AB  - Antiretroviral therapy (ART) adherence is crucial for HIV/AIDS control, yet patient default remains a significant challenge. Defaulter tracing aims to re-engage patients lost to follow-up, but its quantitative impact under varying conditions needs assessment. This study employs numerical simulations of a deterministic compartmental HIV/AIDS model to evaluate the impact of varying defaulter tracing effectiveness (DTeff) and ART retention rates (θ) on epidemic dynamics within Kenya. The model, incorporating susceptible, infected, on-ART, not-on-ART, and under-tracing compartments, was solved using the Runge-Kutta-Fehlberg (RKF45) method with parameters informed by data. Scenarios explored DTeff levels from 45% to 75% and retention rates (θ) from 65% to 85%. Simulation results demonstrate that increasing DTeff significantly reduces the untreated infected population (INARV) and the size of the defaulter population (DTR), while increasing the population maintained on ART (IARV). However, improving the retention rate (θ) showed a significant impact of reducing the need for tracing and the size of the untreated population, while substantially increasing ART coverage. The findings highlight that while effective defaulter tracing is a vital component, particularly when retention is suboptimal, improving ART retention is fundamental for long-term HIV control. This study shows the need for integrated public health strategies that combine robust, proactive retention efforts with efficient defaulter tracing mechanisms to effectively manage the HIV/AIDS epidemic.

VL  - 11
IS  - 1
ER  -

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Author Information

Sammy Maingi

Deparment of Mathematics and Statistics, Machakos University, Machakos, Kenya

Contact Email

http://orcid.org/0009-0005-1960-4896
Benjamin Kikwai

Deparment of Mathematics and Statistics, Machakos University, Machakos, Kenya

http://orcid.org/0000-0002-6741-5011
Mark Kimathi

Deparment of Mathematics and Statistics, Machakos University, Machakos, Kenya

http://orcid.org/0000-0002-5822-8687

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APA Style

Maingi, S., Kikwai, B., Kimathi, M. (2025). Impact of Defaulter Tracing Strategies on HIV/AIDS Dynamics: A Numerical Simulation Study. International Journal of HIV/AIDS Prevention, Education and Behavioural Science, 11(1), 59-67. https://doi.org/10.11648/j.ijhpebs.20251101.17

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ACS Style

Maingi, S.; Kikwai, B.; Kimathi, M. Impact of Defaulter Tracing Strategies on HIV/AIDS Dynamics: A Numerical Simulation Study. Int. J. HIV/AIDS Prev. Educ. Behav. Sci. 2025, 11(1), 59-67. doi: 10.11648/j.ijhpebs.20251101.17

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AMA Style

Maingi S, Kikwai B, Kimathi M. Impact of Defaulter Tracing Strategies on HIV/AIDS Dynamics: A Numerical Simulation Study. Int J HIV/AIDS Prev Educ Behav Sci. 2025;11(1):59-67. doi: 10.11648/j.ijhpebs.20251101.17

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@article{10.11648/j.ijhpebs.20251101.17,
  author = {Sammy Maingi and Benjamin Kikwai and Mark Kimathi},
  title = {Impact of Defaulter Tracing Strategies on HIV/AIDS Dynamics: A Numerical Simulation Study
},
  journal = {International Journal of HIV/AIDS Prevention, Education and Behavioural Science},
  volume = {11},
  number = {1},
  pages = {59-67},
  doi = {10.11648/j.ijhpebs.20251101.17},
  url = {https://doi.org/10.11648/j.ijhpebs.20251101.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijhpebs.20251101.17},
  abstract = {Antiretroviral therapy (ART) adherence is crucial for HIV/AIDS control, yet patient default remains a significant challenge. Defaulter tracing aims to re-engage patients lost to follow-up, but its quantitative impact under varying conditions needs assessment. This study employs numerical simulations of a deterministic compartmental HIV/AIDS model to evaluate the impact of varying defaulter tracing effectiveness (DTeff) and ART retention rates (θ) on epidemic dynamics within Kenya. The model, incorporating susceptible, infected, on-ART, not-on-ART, and under-tracing compartments, was solved using the Runge-Kutta-Fehlberg (RKF45) method with parameters informed by data. Scenarios explored DTeff levels from 45% to 75% and retention rates (θ) from 65% to 85%. Simulation results demonstrate that increasing DTeff significantly reduces the untreated infected population (INARV) and the size of the defaulter population (DTR), while increasing the population maintained on ART (IARV). However, improving the retention rate (θ) showed a significant impact of reducing the need for tracing and the size of the untreated population, while substantially increasing ART coverage. The findings highlight that while effective defaulter tracing is a vital component, particularly when retention is suboptimal, improving ART retention is fundamental for long-term HIV control. This study shows the need for integrated public health strategies that combine robust, proactive retention efforts with efficient defaulter tracing mechanisms to effectively manage the HIV/AIDS epidemic.
},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Impact of Defaulter Tracing Strategies on HIV/AIDS Dynamics: A Numerical Simulation Study

AU  - Sammy Maingi
AU  - Benjamin Kikwai
AU  - Mark Kimathi
Y1  - 2025/06/30
PY  - 2025
N1  - https://doi.org/10.11648/j.ijhpebs.20251101.17
DO  - 10.11648/j.ijhpebs.20251101.17
T2  - International Journal of HIV/AIDS Prevention, Education and Behavioural Science
JF  - International Journal of HIV/AIDS Prevention, Education and Behavioural Science
JO  - International Journal of HIV/AIDS Prevention, Education and Behavioural Science
SP  - 59
EP  - 67
PB  - Science Publishing Group
SN  - 2575-5765
UR  - https://doi.org/10.11648/j.ijhpebs.20251101.17
AB  - Antiretroviral therapy (ART) adherence is crucial for HIV/AIDS control, yet patient default remains a significant challenge. Defaulter tracing aims to re-engage patients lost to follow-up, but its quantitative impact under varying conditions needs assessment. This study employs numerical simulations of a deterministic compartmental HIV/AIDS model to evaluate the impact of varying defaulter tracing effectiveness (DTeff) and ART retention rates (θ) on epidemic dynamics within Kenya. The model, incorporating susceptible, infected, on-ART, not-on-ART, and under-tracing compartments, was solved using the Runge-Kutta-Fehlberg (RKF45) method with parameters informed by data. Scenarios explored DTeff levels from 45% to 75% and retention rates (θ) from 65% to 85%. Simulation results demonstrate that increasing DTeff significantly reduces the untreated infected population (INARV) and the size of the defaulter population (DTR), while increasing the population maintained on ART (IARV). However, improving the retention rate (θ) showed a significant impact of reducing the need for tracing and the size of the untreated population, while substantially increasing ART coverage. The findings highlight that while effective defaulter tracing is a vital component, particularly when retention is suboptimal, improving ART retention is fundamental for long-term HIV control. This study shows the need for integrated public health strategies that combine robust, proactive retention efforts with efficient defaulter tracing mechanisms to effectively manage the HIV/AIDS epidemic.

VL  - 11
IS  - 1
ER  -

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